Listening to the debut album by Foxygen is, at times, a bit like listening to a musical about the 60s and 70s. They zoom between influences, emulating as many rock touchpoints from those decades as you can imagine. You get your Bowie, and your Ray Davies; you get your Dylan and your Jonathan Richman. Yet these Modern Lovers produce a racket that's idiosyncratic enough – and do it with so much vigour and glee – to make We are the 21st century Ambassadors of Peace & Music, overall, a triumph.

Crucially they also know what made the acts they loan from so good. It means they can pinch the best bits of their idols' sounds and create a jukebox of an album that shows how much they love them. At times it seems like a parody but that's precisely part of the band's appeal. It begs the question, how much is arched eyebrow-raised, love-fuelled homage and how much are they brazenly enthralled caricatures, and either way, does it really matter?

The answer seems to lie somewhere in the middle. What's great about Sam France and Jonathan Rado is that they borrow from all these acts and give it back with a massive dollop of passion and outright weirdness. So you get elements of The Kinks, Bowie and the Stones put through a modern filter and you get a glimpse of what would happen if you put all of them together in the 21st century.

Bashed out at a week-long recording session at Richard Swift's National Freedom studio the album is just nine songs long but feels like a sprawling affair. It takes the starting point as the Take The Kids Off Broadway EP but on this, their debut full length, they seem to have honed their songwriting skills (they've certainly had time to do it – they did make 10 records together before unofficially splitting to attend college and only reconvening again in their 20s).

There's also a lot of swagger about the album and, for all the obvious influences, a feeling that this is what comes naturally. 'San Francisco's' Kinks feels and childlike call-and-response chorus, "I left my love in San Francisco/(That's okay, I was bored anyway)/I left my love in a field/(That's okay, I was born in LA)" will stick in your head while first single 'Shuggie', and its ELO shaped chorus, is effortlessly catchy.

It's hard not to play spot the influence throughout the record. 'In The Darkness's' Bowie-ish piano bounce (as well as talk of aliens) and 'No Destruction's' Stones like swagger with its lines about 'smoking pot in the subway' are easy ones; while elsewhere the yelpy madcap title track is Richman channeled in to the 21st century. It ends with the Kinks-hymn 'Oh No 2' and the record finally collapses in on itself under a shower of distortion.

It was a fun journey, and the band, almost brazenly, handpick all the elements they like and meld them into something that feels like their own. Derivative yes, but when it's this fun who cares?