  In the last decade, thanks to the development of sophisticated numerical
codes, major breakthroughs have been achieved in our understanding of the
formation of asteroid families by catastrophic disruption of large parent
bodies. In this review, we describe numerical simulations of asteroid
collisions that reproduced the main properties of families, accounting for both
the fragmentation of an asteroid at the time of impact and the subsequent
gravitational interactions of the generated fragments. The simulations
demonstrate that the catastrophic disruption of bodies larger than a few
hundred meters in diameter leads to the formation of large aggregates due to
gravitational reaccumulation of smaller fragments, which helps explain the
presence of large members within asteroid families. Thus, for the first time,
numerical simulations successfully reproduced the sizes and ejection velocities
of members of representative families. Moreover, the simulations provide
constraints on the family dynamical histories and on the possible internal
structure of family members and their parent bodies.
