This movie's so good that writing this review doesn't interest me all that much. There's nothing I can add to what Captain Phillips already successfully says.
Tom Hanks comes out of moribundity to give us one of the strongest performances of his career. He is refreshingly uncuddly as the titular captain, a smart, professional, but notably ordinary man who, when a freighter he's taking through the Indian Ocean is besieged by a quartet of Somalian pirates, simply does the best he can to keep everyone alive.
Greengrass has created a bookend to his 2006 United 93: both films turn recent true events into intelligent action pictures, emotional but nonjudgmental, thrilling but not exploitative.
Like the terrorists in United 93, the Somalian pirates - led by newcomer Barkhad Abdi, whose dead-eyed stare makes him look like an emaciated Michael K. Williams - are depicted as real people, not merely stock villains. I'm not saying you ever sympathize with them, but you at least see where they're coming from, and why they believe in what they're doing. (Even the film begins like United 93, separately tracking both Phillips and the pirates as they quietly leave their homes and head off toward their fateful confrontation.)
As with all movies based on true stories, perhaps the only serious criticism one might have about Captain Phillips regards its faithfulness to actual events. As for me, I'm not interested in going through the facts with a fine-tooth comb. The point of this film is simply to tell a gripping yarn, and that it does, masterfully.