In September 1996, Weezer released their sophomore album, Pinkerton. It was, in many ways, the turning point in Weezer’s story. Following up an acclaimed debut with some already decade-defining songs to their name, Weezer were approaching their sophomore album as so many big-name bands have in the past. There was a lot riding on this. And the initial reaction wasn’t good. Pinkerton is one of those infamous examples from rock history, an album that was disliked and derided upon its release, only to find a cultish following in subsequent years, only to eventually be (usually) considered Weezer’s finest work and one of the greatest albums of the ’90s. The turnaround in perception of Pinkerton didn’t really matter, though, aside from the album claiming its rightful place in its decade’s hierarchy. The damage it did to Weezer was permanent.

Here was the scope of that damage. Weezer’s insular frontman Rivers Cuomo, who got extremely personal in Pinkerton’s songs, was distancing himself from the album within months thanks to the backlash. There wouldn’t be any new Weezer music until 2001, when they released their second self-titled album, the “Green Album,” with artwork echoing their lauded debut because the whole endeavor was an explicit move towards, in Cuomo’s mind, erasing Pinkerton and getting the band back on the track promised by the “Blue Album.” The phrase “in Cuomo’s mind” is important here, because the man has always zigged and zagged in reaction to his fans, or in reaction to his reaction to his fans. By 2001, people loved Pinkerton. The slick power-pop of “Green Album,” with all of Cuomo’s personal songwriting sucked out? That’s not what Weezer fans wanted, either. It’s now pretty easy to rank it as one of the band’s worst albums.

That is, essentially, how much of Weezer’s career has unfolded. A beginning defined by dizzying highs, followed by all sorts of course-corrections and left turns along the way. Cuomo has tried going back to basics, he has tried not writing about himself; he has tried experimenting with pop; he eventually really did get back to something like the basics; he wrote some embarrassing but very successful songs and he wrote lesser-known tracks that his fans loved. It’s a mess. And it all exists in the long shadow of Pinkerton, the album that broke Cuomo at the time but also the album that his fans now adore beyond anything he’s done since. The weight of that, the frustration of trying to create in the wake of that, must be nearly paralyzing.

Like Oasis, another ’90s great, Weezer’s story has long since been defined as such: a meteoric, genius beginning, a complete flameout, and then a protracted latter-era equally populated by ill-fated stylistic detours and reliable, almost workmanlike exercises in what they were first known to do best. The highs, where they exist, are less dizzying, and sometimes it seems as if only diehards have stuck around to dig through it all for the gems.

And, fair enough, Weezer’s run from 2001 to today is clogged with persistent mediocrity and the occasional disaster, making that search for gems seem harder than it really is. Sure, they will never make another “Blue Album” or Pinkerton. How could they? But, really, why should they? The unfortunate trope of bands that start the way Weezer did is that they’ll never live up to that past, no matter how they attempt to appease old fans. The unfortunate fallout is that everything they do will be forever judged against the music they made when they were young and raw, an unfair standard that’s ever-present in pop music but gets applied to groups like Weezer and Oasis — and the Strokes and Smashing Pumpkins and so on — far more aggressively.

Cuomo is a furiously prolific songwriter at times; there are a few moments in Weezer’s history when the albums arrived a year and change apart, and there’s leftover material beyond that. This, it seems, is another reason Cuomo received the ire of his fans: He lost his way, and kept plugging along stubbornly. That’s how it would appear. Along the way, it could feel like he was trolling. Along the way, he also wrote some of the best Weezer songs.

There are some rough low points in Weezer’s discography. There’s no getting around that. But just as Cuomo changed his position too severely in response to Pinkerton’s initial failure, our perception of the band’s output shifted too severely in response to that album’s reclamation. Plenty of — if not most — bands put out their classic records in the first few years of their existence, and continue on in that shadow. The injustice in a situation like Weezer’s is that nobody gives them credit for all the very good stuff that came later, just because it isn’t classic.

Upon the release of Weezer’s new LP Pacific Daydream — the intermission between 2016’s “White Album” and the forthcoming “Black Album,” which might be out as soon as May — we decided to take a look back at some of the highlights from Weezer’s career since Pinkerton. After a pretty scattershot ’00s, the band has started to win people over again, coaxing fans back with 2010’s Hurley, delivering a post-Pinkerton highpoint in 2014’s Everything Will Be Alright In The End, and continuing on through this new solidly consistent phase with the “White Album.” Maybe Pacific Daydream will put a dent in that. But being invested in Weezer means knowing that there will be highs and lows, and within that back and forth there will always be well-crafted songs that are worth returning to. Here are 16 of those songs below.

“Hash Pipe” (from the “Green Album,” 2001)

The problem weighing down most of “Green Album” isn’t that much of it is bad, per se. It’s just kinda there. There are songs on there where you can forget what you listened to as soon as they end. “Hash Pipe” is not one of those songs. Between its chugging verse riff, its thrashing chorus, and Cuomo’s freaked-out high-pitched vocals and a few performative grunts, the song might not have the emotive wallop of Weezer’s best ’90s material, but it is one of the finest examples of how economically and precisely 21st century Weezer are able to deploy unforgettable hooks.

“Island In The Sun” (from the “Green Album,” 2001)

Some people loathe “Island In The Sun.” And that’s understandable. A mellow sing-song ballad, it’s one of those mainstream alt-rock outings that crossed over into that realm of songs built for commercials and idle shopping-mall excursions.The simplicity of “Island In The Sun” is really effective, though; unless you’ve simply heard it far too many times, it’s an effortlessly catchy Weezer track. And as far as pop crossovers in the band’s career, they’ve committed far worse sins.

“Dope Nose” (from Maladroit, 2002)

“Dope Nose” was written in the same sitting as “Hash Pipe,” and it has the same runaway sugar-high energy as its predecessor. (Or rather, in this case, it has the same Ritalin-and-tequila energy.) A single from “Green Album” successor Maladroit, “Dope Nose” almost feels like a direct sequel to “Hash Pipe” — it’s more bubbly, but it has the same crunchy infectiousness. When Weezer play either of them these days, the crowd reaction is huge, as if these are the old classics. Which, essentially, is what they’ve become. Whatever you think of their respective albums, these two songs are some of the definitive Weezer singles of the ’00s and beyond.

“Keep Fishin'” (from Maladroit, 2002)

Maladroit has the reputation as being the knottier companion to “Green Album,” but there’s still some prime-Cuomo songwriting when it comes to pleasantly riffy earworms, like the aforementioned “Dope Nose” and the bouncy “Keep Fishin.'” This one’s also a good entry in Weezer’s history of memorable videos, with very special guest stars in the form of the Muppets.

“Perfect Situation” (from Make Believe, 2005)

Make Believe is one of Weezer’s worst albums. From one famously grating lead single to a host of anonymously polished radio-rock ventures, it kicked off Weezer’s disastrous run through the second half of the ’00s. It’s mostly irredeemable, but it isn’t completely without worth. Sitting right there next to “Beverly Hills” was its flipside, “Perfect Situation.” Where the former was an unnatural and damaging dance towards mainstream approaches, “Perfect Situation” functioned similarly, the main difference being that it was good. From the piano propulsion of its verses to the catharsis of its mostly wordless chorus, “Perfect Situation” was an undeniably well-crafted single, a glimpse of what an adventurous, 30-something Weezer might’ve sounded like if the other songs weren’t duds.

“This Is Such A Pity” (from Make Believe, 2005)

When one of the best songs on your mid-’00s album sounds like the Killers’ impression of the Cars, it is probably not an auspicious signal for what else is on there. And, well, it wasn’t! But despite the fact that you can poke fun at “This Is Such A Pity,” it was also one of the glimmers of hope on Make Believe. A streamlined and synth-laced rocker, it’s another “What if?” moment in Weezer’s catalog; for whatever reason, similar experiments of theirs have usually gone awry, but “This Is Such A Pity” is casually lovable.

“The Greatest Man That Ever Lived (Variations On A Shaker Hymn)” (from the “Red Album,” 2008)

The “Red Album” has some real clunkers, and some of Weezer’s most irritating songs. It also has “The Greatest Man That Ever Lived (Variations On A Shaker Hymn),” a beloved fan favorite amongst post-Pinkerton Weezer. Fittingly given its title, “The Greatest Man…” is one of the epics in Weezer’s catalog, a rush through fragments and genres that somehow transcends the threat of medley. Instead, it’s a wild journey, pulling the listener along through places and eras before the climactic conclusion of a Beach Boys-esque chorus giving way to one last grunge outburst.

“Troublemaker” (from the “Red Album,” 2008)

This is one of those songs people say Rivers Cuomo can write in his sleep, and that’s totally true. The thing about “Troublemaker” is that it arrived in an era otherwise defined by some of Weezer’s most disappointing misadventures and some of their most autopilot rock songs. Granted, you could call “Troublemaker” autopilot, I suppose. But the difference whether a latter-day Weezer rocker is good or bad is the hooks, and “Troublemaker” definitely has those. It wasn’t enough to save the “Red Album” or avoid the coming wreckage of Raditude, but it’s a straightforward and addicting cut from that time, and remains a welcome presence whenever the band plays it live today.

“Brave New World” (from Hurley, 2010)

By the end of the ’00s, things looked pretty grim for Weezer. While their missteps could often be written off as middle-of-the-road most of the time, they released some truly humiliating material on 2009’s Raditude. When they returned less than a year later with an album named for a Lost character, with said Lost character on the cover, it seemed like they were straight-up trolling. Then Hurley turned out to be pretty good! Songs like “Brave New World” restored a lot of the humanity that had been missing on albums like Make Believe, and there’s real urgency in the track’s chorus, perhaps derived from the band regaining a bit of fire.

“Ain’t Got Nobody” (from Everything Will Be Alright In The End, 2014)

This is where Weezer really got things back on track. Everything Will Be Alright In The End was the band’s strongest and most consistent album in years, a record anchored by three themes: romantic relationships, father-son relationships, and artist-fan relationships. Perhaps honing in on some of his core topics helped refocus Cuomo, but the basic fact is that the songs were there. The whole thing kicked off with “Ain’t Got Nobody,” a stomping rocker where Cuomo danced between about half a dozen memorable melodies.

“The British Are Coming” (from Everything Will Be Alright In The End, 2014)

“The British Are Coming” is an interesting mix. On one hand, it feels like something different for Weezer: Hitting middle age, the verses and bridge are light, jangly, and pretty, and while the song has fuzz around the edges it doesn’t feel the need to explode into a big alt-rock moment. At the same time, the way Cuomo swings himself up into the chorus sounds like some old-school Weezer. It’s one of the best songs on Weezer’s best recent album, partially because it’s a great example of how the band could settle into a new groove and age more gracefully than Cuomo’s “Red Album”-era mustache might’ve suggested.

“Foolish Father” (from Everything Will Be Alright In The End, 2014)

It’s funny that Everything Will Be Alright In The End marked Weezer’s third collaboration with the Cars’ Ric Ocasek. Considering that they bottled lightning on the “Blue Album” and then presented polished-but-diminished returns on “Green Album,” the third project could’ve gone either way. The songs on Everything Will Be Alright In The End feel more alive than most of the material on “Green Album,” a song like “Foolish Father” being a prime example. It wouldn’t be hard to imagine a version of this song on “Green Album,” but here it actually leaves a mark.

“Do You Wanna Get High?” (from the “White Album,” 2016)

How do you nearly squander the goodwill accrued by an album like Everything Will Be Alright In The End? You introduce the next album with a song like “Thank God For Girls.” That song is a low-point on the otherwise strong “White Album,” and thankfully the band soon showed us another side of the album with “Do You Wanna Get High?” A slithering-then-cooing track, it’s one of those places where Weezer sound a lot like their old selves, but in a way that feels like a natural progression. There’s almost a weathered quality to the chorus — something you wouldn’t normally associate with the ever-youthful Cuomo — like the song’s titular offer comes after a few too many years of partying. On an album dedicated to the California dream, this added a little texture, a little complication, playing out like a sinister little detour.

“King Of The World” (from the “White Album,” 2016)

Like “Troublemaker,” “King Of The World” is another song that sounds pretty much like Cuomo could write it in his sleep. And like “Troublemaker,” the thing that makes “King Of The World” stand out is that Cuomo must’ve had a good night of sleep. A track that strongly recalls Weezer’s early days, “King Of The World” crests into one of the biggest and most convincing choruses of their recent years. It’s a huge, gratifying rock song for a few reasons, not least of which being the realization that Weezer still have huge, gratifying sing-alongs in them.

“L.A. Girlz” (from the “White Album,” 2016)

What Beach Boys-indebted, California-concept album from Weezer would be complete without a song called “L.A. Girlz” that also has a lyric where Cuomo laments LA girls not wanting to talk to him by telling them “Please act your age.” The whole thing is very Weezer-esque, from Cuomo’s self-aware social anxiety to the crunchy music. And like much of the “White Album,” it helped solidify the post-EWBAITE feeling that Weezer were in a good, fruitful spot.

“Weekend Woman” (from Pacific Daydream, 2017)

Right on the heels of “White Album,” we have Pacific Daydream, which finally arrived last week after a trail of singles that goes all the way back to the release of “Feels Like Summer” in March. Another California vision of an album, Pacific Daydream oscillates between a few polarities — namely, pop excursions that feel like an awkward look for aging Weezer while not being as embarrassing as what they were up to a decade ago, and material that feels like a logical extension of “White Album” while also exploring new territory. And while “Feels Like Summer” may have found Weezer some new pop success, the most immediately impressive lead single from Pacific Daydream was “Weekend Woman,” a breezy West Coast jam that boasts one of Cuomo’s most sneakily brilliant choruses of recent times. Sunny and wistful and yearning all at once, it captures the conflict inherent to the promise of places vs. their reality. It has the sound of nostalgia pregnant with the awareness that nostalgia can be a hindrance. “Weekend Woman” is a gorgeous track, and though it’s surrounded by some more questionable material, it’s enough to remind us that latter-day Weezer can still off-handedly deliver very convincing arguments for why we should still believe in them.