TITLE: Status of mixed motives
QUESTION [7 upvotes]: From the wikipedia page:
http://en.wikipedia.org/wiki/Motive_(algebraic_geometry)
it appears that the category of Mixed motives $MM(k)$ over a field $k$ is still conjectural; but there is a good derived category $DMM(k)$ already constructed for this. 
What is a good reference for this construction, and why this derived category is the "suitable" one.

REPLY [6 votes]: As a supplement to T..'s nice answer, let me write something that is more of a cultural remark than a direct answer to the question:
Many people learnt about the yoga of mixed motives by reading Deligne's article
on the thrice punctured sphere.  (This was certainly the case for me; and a hat-tip to Quomodocumque for providing the link.) 
This article helps explain what one should expect from the category of mixed motives, and thus helps one recognize the (or perhaps a) correct construction when one sees it.