Simply put, the story of Fast and Furious is not in the order that the movies are released. A bit of this post is a little speculative since one of the movies is in pre-production, but the cast has already been confirmed. Obviously there are some spoilers below tying it all together.
The first movie - The Fast and The Furious (2001), ends with Brian O'...
Here is a full Fast and Furious Timeline as
The Fast and the Furious (2001)
Turbo Charged Prelude (2003 Video)
2 Fast 2 Furious (2003)
Los Bandoleros (2009 Short Film)
Fast & Furious (2009)
Fast Five (2011)
Fast & Furious 6 (2013)
The Fast and the Furious: Tokyo Drift (2006)
Furious Seven (2015)
The Fate of the Furious
At the end of Fast 6 they show the same clip from Han dieing in Tokyo Drift, but you see Jason Statham get out of the car that hit Han's. So seven will take place with Dom going to Tokyo (assuming) since he shows up in the end of Tokyo drift
Tokyo Drift felt really out of place in the timeline. Nothing seemed to add up because it was assumed the events occurred either completely independent of Dom's realm, or perhaps directly after 2 Fast 2 Furious based on Dom's appearance at the end of the film.
The writers did an amazing job re-introducing Han into the big picture by giving him a small yet ...
Watch the movies in this order if you want to know:
The Fast And The Furious 
2 Fast 2 Furious 
Fast And Furious 
Fast Five 
Fast and furious 6  (don't forget to watch the mini clip at the end!)
The Fast And The Furious: Tokyo Drift 
Why do people become "fast and furious"? It's not to break speed records. They're thrill seekers. They just happen to center their thrills (mostly) on fast cars, but they do get off on robbing people. They've shown that time and time again, from small gas trucks to the wealthiest person in an entire country.
Han was chasing the thrill of ripping off the ...
Based on @BlueMoon93's comment, it would probably be safe to say that it can be attributed to Tokyo Drift being non-canon (partially anyway) and perhaps a mistake on writer's part in Fast & Furious 6 -
Han becomes rich after Fast Five which was released in 2011, Tokyo Drift had come out five years before in 2006. The film writers, at the time of ...