[Ke3] B. Keller, On differential graded categories, preprint (available on Keller’s webpage).
Toen: Lecture on DG-categories. File Toen web unpubl swisk.pdf. Treats basic theory, localization, relation to model cats, functorial cones, K-theory and Hochschild cohomology, and descent problems.
Toen: The homotopy theory of dg-cats and derived Morita theory. File Toen web publ mapdgcat.pdf.
Toen and Vaquie: Moduli of objects in dg-cats: Discusses triang cats with some finiteness assumptions, admitting a dg-enhancement. File Toen web publ ttt.pdf.
http://ncatlab.org/nlab/show/dg-category
arXiv:0908.4187 Uniqueness of enhancement for triangulated categories from arXiv Front: math.AG by Valery A. Lunts, Dmitri O. Orlov The paper contains general results on the uniqueness of a DG enhancement for triangulated categories. As a consequence we obtain such uniqueness for the unbounded categories of quasi-coherent sheaves, for the triangulated categories of perfect complexes, and for the bounded derived categories of coherent sheaves on quasi-projective schemes. If a scheme is projective then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded derived categories of coherent sheaves. These results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product.
nLab page on DG-category