LATER THIS YEAR, Dreamgirls and Twilight director Bill Condon will release The Fifth Estate, a drama about WikiLeaks founder Julian Assange. Wearing an appropriately garish platinum wig, everybody's favorite Sherlock and second-favorite Khan, Benedict Cumberbatch, will play Assange, and my guess is he'll do a pretty great job: Few actors could convey Assange's weird blend of menace and likeability, and Cumberbatch is one of them. But even if The Fifth Estate turns out well, it probably won't be better than We Steal Secrets: The Story of WikiLeaks, the latest documentary from Alex Gibney (Enron: The Smartest Guys in the Room, Taxi to the Dark Side, Freakonomics).

In looking at WikiLeaks from its founding to its meltdown, Gibney patches together a tale that's mostly about Assange, but also about Private Bradley Manning—a soldier and a tech geek who, depending on whom you ask, is either a traitor or a hero.

The fact that Manning's court-martial trial began earlier this week—hacker Adrian Lamo, who turned Manning in to the feds (and is one of the more off-putting interviewees in We Steal Secrets), testified against Manning on Tuesday—is only part of what makes Gibney's film feel urgent and current. The other part is that the issues roiling beneath We Steal Secrets are ones we aren't going to solve anytime soon. The primary concern of We Steal Secrets—how the internet has changed the speed and flow of information, and how information can change the world—is one we'll be dealing with for the rest of our lives. Luckily for most of us, we won't have to deal with it the way Assange and Manning have.

Boasting interviews with just about everyone—except Assange and Manning—We Steal Secrets pulls from news footage, documents, and chat transcripts, and from the words of journalists, hackers, intelligence experts, CIA directors, and those who used to work alongside Assange (most of whom look incredibly young). It's a sprawling, unpredictable infodump—even Lady Gaga turns up—and the result is formless, but engrossing. It cuts deep and often, but most reliably when it comes to statements that, intentionally or not, define the people involved: "I'm fond of the phrase 'lights on, rats out,'" Assange proclaims in an old interview, as if declassifying information is really that simple. Elsewhere, Manning (both sexually and ethically confused) confides to a man who will one day turn him in. He chats in nerdy techspeak: "The CPU," he types about himself, "is not made for this motherboard."

Manning is the nerd who gave "transparency radical" Assange a mother lode of classified documents and ended up in solitary confinement at Quantico; Assange is the nerd who blasted those files out to the world before being accused of sex crimes and hiding out in an Ecuadorian embassy, where he's been for the past year, ducking extradition. From the uprisings of the Arab Spring to Matthew Broderick madly typing away in WarGames, Gibney finds all kinds of connections, while also—and from a distance—mucking about in the consciences of these two men, neither of whom comes across particularly well. (Neither do the Bush and Obama administrations, nor the old-media journalists who briefly teamed up with WikiLeaks.) It's a disturbing and complex story—and one that's still going, and still growing increasingly more complicated. Gibney doesn't try to provide answers, but he does offer information—and if there's one thing Manning and Assange have taught us, it's that information should never be underestimated.