Asteroids formed in a dynamically quiescent disk but their orbits became gravitationally stirred enough by Jupiter to lead to high-speed collisions. As a result, many dozen large asteroids have been disrupted by impacts over the age of the solar system, producing groups of fragments known as asteroid families. Here we explain how the asteroid families are identified, review their current inventory, and discuss how they can be used to get insights into long-term dynamics of main-belt asteroids. Electronic tables of the membership for 122 notable families are reported on the Planetary Data System node. See related chapters in this volume for the significance of asteroid families for studies of physics of large-scale collisions, collisional history of the main belt, source regions of the near-Earth asteroids, meteorites and dust particles, and space weathering.