I would like to know how derived categories (in particular, derived categories of coherent sheaves) can give results about "Traditional Algebraic Geometry". I am mostly interested in classical problems. For example: moduli spaces problems, automorphism groups of varieties, birational classification of varieties, minimal model program and so on.

Furthermore, I would also be interested to know about theorems that are more aesthetically pleasing being stated in the derived category language. For instance, I think Serre duality can be generalised to singular varieties through derived categories.

Any reference about results is very welcome.