Status of mixed motives 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.
 A: The Wikipedia references are a reasonable starting point in the sense that some of them contain Voevodsky's construction(s) and related expositions.  Beyond that the literature on motives is enormous and difficult and relies on many ideas that are not apparent from the papers themselves -- not to mention unpublished letters and oral tradition found in a few major mathematical centers.  The state of documentation is far better in the internet era but this is still a highly technical field that is difficult to penetrate by casual reading.  In one respect the main breakthrough made by Voevodsky is that he created a theory with a framework that can be learned (e.g., by topologists) knowing scheme theory and a bounded number of other things, whereas before that motives were considered a pinnacle of inaccessible mystery, or a foundation-less heuristic used informally.
As for what is "suitable", Voevodsky proved the universality of motivic cohomology as defined in his approach; in the 2-category of homology theories satisfying some axioms, he constructs an initial object (similar to characterizing singular homology as the universal model of Eilenberg-Steenrod axioms).  Also, he builds a motivic homotopy theory with analogies to the topological theory, and not "only"(!!) the motivic homology and cohomology.  There are other respects in which his approach is better motivated (so to speak) or conceptual compared to other approaches.  (Grothendieck's approach is also conceptual but assumes Standard Conjectures and the work on mixed motives was not published.)   So although nobody knows the ultimate construction of mixed motives, Voevodsky's approach is the leading contender at present.
A: 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. 
