  It has recently become possible to form molecules in ultracold gases of
trapped alkali metal atoms. Once formed, the molecules may undergo elastic,
inelastic and reactive collisions. Inelastic and reactive collisions are
particularly important because they release kinetic energy and eject atoms and
molecules from the trap. The theory needed to handle such collisions is
presented and recent quantum dynamics calculations on ultracold atom-diatom
collisions of spin-polarised Li + Li_2, Na + Na_2 and K + K_2 are described.
All these systems have potential energy surfaces on which barrierless atom
exchange reactions can occur, and both inelastic and reactive rates are very
fast (typically k(inel) > 10^{-10} cm^3 s^-1 in the Wigner regime).
