  Theories of how galaxies, the fundamental constituents of large-scale
structure, form and evolve have undergone a dramatic paradigm shift in the last
few decades. Earlier views were of rapid, early collapse and formation of basic
structures, followed by slow evolution of the stellar populations and steady
buildup of the chemical elements. Current theories emphasize hierarchical
buildup via recurrent collisions and mergers, separated by long periods of
relaxation and secular restructuring. Thus, collisions between galaxies are now
seen as a primary process in their evolution. This article begins with a brief
history; we then tour parts of the vast array of collisional forms that have
been discovered to date. Many examples are provided to illustrate how detailed
numerical models and multiwaveband observations have allowed the general
chronological sequence of collisional morphologies to be deciphered, and how
these forms are produced by the processes of tidal kinematics, hypersonic gas
dynamics, collective dynamical friction and violent relaxation. Galaxy
collisions may trigger the formation of a large fraction of all the stars ever
formed, and play a key role in fueling active galactic nuclei. Current
understanding of the processes involved is reviewed. The last decade has seen
exciting new discoveries about how collisions are orchestrated by their
environment, how collisional processes depend on environment, and how these
environments depend on redshift or cosmological time.
