  Over the last few years, wall-crossing for Bridgeland stability conditions
has led to a large number of results in algebraic geometry, particular on
birational geometry of moduli spaces.
  We illustrate some of the methods behind these result by reproving
Lazarsfeld's Brill-Noether theorem for curves on K3 surfaces via wall-crossing.
We conclude with a survey of recent applications of stability conditions on
surfaces.
  The intended reader is an algebraic geometer with a limited working knowledge
of derived categories. This article is based on the author's talk at the AMS
Summer Institute on Algebraic Geometry in Utah, July 2015.
