Paul Thomas Anderson’s “One Battle After Another” is an exciting, goofy and deadly serious big-screen no — a no to complacency, to oppression, to tyranny. It’s a carnivalesque epic about good and evil, violence and power, inalienable rights and the fight against injustice; it’s also a love story. The film speaks to the failures of the past and of the present but insists on the promise of the future. It’s brilliantly directed, but what makes it exhilarating is that it engages with its moment as few American fiction films do. It feels shockingly urgent. It’s also snort-out funny, even when its laughs tremble with rage.

“One Battle After Another” charts the misadventures of a glorious fool, Bob Ferguson — Leonardo DiCaprio wholly rising to the buffoonish occasion — a revolutionary foot soldier turned hunted terrorist, underground fugitive and doting single dad. Set largely in the present, the story takes flight some 16 years earlier during Bob’s explosive tenure in the French 75, a radical group (presumably phony!) that shares its name with a field gun and a cocktail that Humphrey Bogart’s nightclub serves in “Casablanca.” The group’s beliefs are pretty straightforward (equality, freedom), if fuzzy on specifics, and Anderson doesn’t spell out its revolutionary ideology. Like his characters, he generally prefers putting theory into action.

The story’s fulcrum is the love between Bob and Perfidia Beverly Hills (a galvanic Teyana Taylor), a charismatic member of the French 75. Gutsy and uncompromising, Perfidia cuts through the world like a knife. Early on, Bob eagerly follows her lead during the group’s attack on a migrant detention center where, under the cover of night, they and the other insurgents disarm the military guards and liberate a crowd of men, women and children. It’s there, too, that Perfidia first encounters her nemesis, Col. Steven J. Lockjaw (a great Sean Penn), whom she easily overpowers with a drawn gun and unusual command: She orders the seated Lockjaw to get up, all the way up, a directive that he obeys with an erection that comically pitches a tent in his pants.

It’s a crucial moment and absurd sight, which Anderson exploits for maximum ridiculousness by filming the erection from below so that it looms in the shot, emphasizing Lockjaw’s helplessness before Perfidia. He is no longer in control of the detainees or his own body, and he certainly isn’t in control of her. Perfidia has effectively disarmed Lockjaw, which instigates a mad, perverse desire for her. In forcing Lockjaw to comply, she has challenged a regime of power, one that traces back to the violent sexual exploitation of enslaved Black women by white men, and which the movie’s villains want to maintain. Lockjaw will spend the rest of the film trying to reassert his supremacy.

“One Battle After Another” was inspired by “Vineland,” Thomas Pynchon’s 1990 novel, which Anderson has liberally borrowed from to his singular ends. The novel opens in 1984, the year that Ronald Reagan’s won his second term as president and in the wake of “the Nixonian Repression.” Time has marched on for its humorously named post-1960s survivors (Anderson invents his own cartoon monikers), yet while “the personnel changed, the Repression went on, growing wider, deeper, and less visible,” a character observes. (In a 2015 interview with the novelist Steve Erickson that took place in Trump Tower, Anderson talked about “Vineland” — “near the top for me,” he said — and that he’d either adapt it “or just rip a lot of it off.”)

Anderson doesn’t name names in “One Battle After Another,” and I don’t remember hearing anyone calling out any current politicians. Even so, it is circa 2009, the year that Barack Obama’s first term began, when the French 75 takes over the detention center during a propulsive, intricately staged and shot sequence that sets the heady tone and rapid pace. The group’s members are elated by the raid, as turned on by their success as Lockjaw is by Perfidia. “¡Viva la revolución!” Bob cries out as they make their getaway, a battle cry that resounds as he and Perfidia hook up, rob banks, have a daughter, split up, go on the run. Everything falls apart, and Bob ends up adrift in a cannabis fog.

Anderson rarely lets up on the gas in “One Battle After Another,” though he eases up somewhat when the story shifts to the present. Having gone underground years earlier, Bob is now living with his daughter, Willa (the newcomer Chase Infiniti), in a house in Northern California (natch), that halcyon land of redwoods, dope and paranoia. There, he drinks a lot of booze and tokes a lot of weed — smoke wafting around his permanently confused face, his tiny ponytail hanging flaccidly like an emblem of his impotence. His ardor is gone and so is Perfidia, who exited long ago. To pass the time, he watches Pontecorvo’s 1966 film “The Battle of Algiers” — he mouths the words — about the Algerian struggle for independence.

It’s easy to laugh at Bob, but there’s a well of pathos in his personal and generational failures. Anderson isn’t interested in soliciting your pity, however (that would be too cheap), and both the character and DiCaprio’s physically outsized performance — it’s a madcap tour de force — keep you from going soft on Bob. You watch the character but never get deep in his head, partly because Bob never does either. He’s a supremely unconscious man who’s notably only roused to take action against oppression when it affects him personally, which it does when Lockjaw returns, scowl and ramrod posture intact. (Penn’s walk suggests that the rod is firmly planted in the character’s backside.)

What redeems Bob is love: his for Willa and hers for him. That love lights up the rest of the movie like a beacon. It has bonded father and daughter, creating a conspiracy of two. It’s helped make Willa who she is, and it has probably kept Bob from disappearing entirely. Love is what forces him out of his refuge and his entropy when Lockjaw — now backed by a shadowy group of Christian white supremacists called the Christmas Adventurers Club — violently re-enters the scene, imperiling Willa. The movie takes another turn as Bob and Willa each flee Lockjaw, splintering the story into separate sections that eventually converge. Things then get even more complicated, and scary.

Anderson’s gift for putting a great many pieces into play is fully on display in “One Battle After Another,” including with his superb cast. The supporting players include Regina Hall as Deandra, one of the original French 75, and Benicio Del Toro as Sensei Sergio St. Carlos, a martial-arts instructor who helps run an underground railroad for migrants. In a sly bit of casting, Tony Goldwyn — a star of the pulpy TV series “Scandal” — shows up as one of the leaders of the Christmas Adventurers Club. In that show, which began airing in 2012, the white president (Goldwyn) is having a passionate affair with Kerry Washington’s Black crisis-management expert, a romantic fantasy that often felt very much of its ostensibly post-racial moment.

“One Battle After Another” offers up another imaginary world, though one that, despite all the nonsense names and flights of fancy, looks and feels more like life than not. Not everything fits together seamlessly in the film, which only strengthens its realism; after watching it twice, I am still sifting through its ideas and its images, still thinking about power and race and sex, and whether Perfidia really gets her due, as I continue savoring the high that the movie produces. There are few filmmakers working today who are as skilled as Anderson, and fewer still who could — with the image of a heavily pregnant Black revolutionary firing a machine gun — create a cry from the heart that’s also a crystallizing image of resistance. It’s one for the ages, wild and thrilling, and every bit as American as the red, white and blue.

One Battle After Another
Rated R for gun violence and language. Running time: 2 hours 41 minutes. In theaters.