Most of this review has focused on collisions of cold, trapped atoms in a light field. Understanding such collisions is clearly a significant issue for atoms trapped by optical methods, and historically this subject has received much attention by the laser cooling community. However, there is also great interest in ground-state collisions of cold neutral atoms in the absence of light. Most of the early interest in this area was in the context of the cryogenic hydrogen maser or the attempt to achieve Bose–Einstein condensation (BEC) of trapped doubly spin-polarized hydrogen. More recently the interest has turned to new areas such as pressure shifts in atomic clocks or the achievement of BEC in alkali systems. The actual realization of BEC in 87Rb [15], 23Na [103], 7Li [56, 57], 4He* [310, 330] and H [138] has given a tremendous impetus to the study of collisions in the ultracold regime. Collisions are important to all aspects of condensates and condensate dynamics. The process of evaporative cooling which leads to condensate formation relies on elastic collisions to thermalize the atoms. The highly successful mean field theory of condensates depends on the sign and magnitude of the s-wave scattering length to parameterize the atom interaction energy that determines the mean field wavefunction. The success of evaporative cooling, and having a reasonably long lifetime of the condensate, depend on having sufficiently small inelastic collision rates that remove trapped atoms through destructive processes.