For a gritty film about the drug trade to succeed in this post-“Traffic” world, it will need what “Traffic” lacked: heart and humanity.

“Blow” has it, taking us through the dizzying life of real-life trafficker George Jung and telling the drug story through the eyes of a man who lived it. The effect is visceral and engaging, and the film is often wryly, ironically funny as well as achingly tragic.

Johnny Depp plays George, a working-class kid from a Boston suburb who heads to California’s Manhattan Beach in 1968 at the age of 18. He and his fat friend Tuna (Ethan Suplee) discover marijuana, and the enterprising George starts selling it, with help from a gay supplier named Derek (Paul Reubens).

Soon he’s using his stewardess girlfriend Barbie (Franka Potente) to funnel the stuff back to Massachusetts, where his friends have set up a franchise operation for him.

Time passes. George goes to jail — “crime school,” he calls it: “I went in with a bachelor’s in marijuana and came out with a doctorate in cocaine.” His cellmate is Diego (Jordi Molla), who has ties to a Colombian cocaine operation. Once they’re both set free, they get right to work establishing an extremely lucrative operation. George also gets to work wooing and marrying Colombian hottie Mirtha (Penelope Cruz).

The film’s sprawling narrative never settles down. It’s hard to tell when, if ever, we’re going to stay in one locale or with one group of supporting characters for the long haul. That time never does come, in fact, which adds to the movie’s melancholy tone: Just like George, we shouldn’t get too attached to anyone, because they’re not going to be around forever.

Ray Liotta (making his third film appearance this year) and Rachel Griffiths play George’s parents. Griffiths’s accent sounds like a left-over from “Thirteen Days,” but Liotta is fantastic as George’s dad. He always told his son that money isn’t everything — but now that George is financially well-off, he has a certain pride in knowing the boy made it better than his old man did. Depp and Liotta have an unexpected chemistry as father and son.

Johnny Depp, who actually is as brooding and soulful as some people think Leonardo DiCaprio is, gives one of his best performances yet as George. He’s an intriguing anti-hero, earning sympathy and never coming across as the major criminal he is.

I have issues with the final third of the movie, which gets to be a fairly standard family melodrama with George’s demanding wife and precious young daughter. That said, I found it rather touching, too. I’m a sucker for a flawed man trying to do right by his little girl. I guess we all have our vices.

B+ (; R, abundant harsh profanity, some strong.)