  These are expended notes of my talk at the summer institute in algebraic
geometry (Seattle, July-August 2005), whose main purpose is to present a global
overview on the theory of higher and derived stacks. This text is far from
being exhaustive but is intended to cover a rather large part of the subject,
starting from the motivations and the foundational material, passing through
some examples and basic notions, and ending with some more recent developments
and open questions.
