This "virtuosic", politically charged triumph is "horrifying yet ridiculously funny". It's rare to see such an ambitious film work so smoothly.

Paul Thomas Anderson is the brilliant mind and Leonardo DiCaprio the emotional heart of this timely, audacious comic-action-drama One Battle After Another. As Bob, a former radical now content to drink and smoke all day long, DiCaprio races around in a plaid bathrobe and a beanie trying to rescue his abducted teenage daughter. It's a funny turn, but the love and fear in his eyes tell you how deeply Bob feels. That is just one element of the film, which is also full of car chases, militias, shadowy organisations, loyalties and betrayals, all fused in a story that pulls you along from start to finish and that is jolting in its political immediacy. It's rare to see such an ambitious film work so smoothly, but then, one of Anderson's signatures is his ability to coolly control raucous, sprawling stories.

Throughout his career, he has had a distinctive voice – crisp, clear, elegant and funny – but those qualities pop up in a variety of styles, including the intense There Will Be Blood (2007) and the elegant Phantom Thread (2017). One Battle After Another brings together several strands, particularly the comic glee of Boogie Nights (1997) and the juggling act of multiple stories in Magnolia (1999).

It's also his second film to be influenced by a Thomas Pynchon novel. Inherent Vice (2014) was the first, and One Battle After Another was inspired by Pynchon's 1990 novel, Vineland, about a leftover 1960s radical, two decades on. Anderson has borrowed just a whiff of the plot, updated it to the present and created entirely new characters, yet he has kept the soul of a Pynchon novel: there are hints of it in some cartoonish names and in the antic comedy. Most importantly, Pynchon was sending up nefarious quasi-government organisations in his novels – as Anderson does here with comic yet deadly-serious finesse – long before conspiracy theories went mainstream.

The taut early scenes are set at a holding centre for immigrants, where military guards prowl behind chain-link fences, in images clearly meant to echo those seen on the news. A fictional group called the French 75 infiltrate the site to announce the revolution. Among its members, Perfidia Beverly Hills (Teyana Taylor) is tough and uncompromising. Bob is their explosives expert and her lover. The film is nuanced enough to understand the radicals' goals, yet it makes no excuses for their violent actions.

At the immigrant centre, Perfidia encounters the sinister Captain Steven Lockjaw, a character as broadly drawn as his name. Sean Penn makes him thoroughly convincing as a sexual creep who later bullies and blackmails her, and who admits that he is drawn to her because she is black. Perfidia soon goes........

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