  We provide a taxonomy of dynamical supersymmetry breaking theories, and
discuss the cosmological implications of the various types of models. Models in
which supersymmetry breaking is produced by chiral superfields which only have
interactions of gravitational strength (\eg\ string theory moduli) are
inconsistent with standard big bang nucleosynthesis unless the gravitino mass
is greater than $\CO(3) \times 10^4$ GeV. This problem cannot be solved by
inflation. Models in which supersymmetry is dynamically broken by
renormalizable interactions in flat space have no such cosmological problems.
Supersymmetry can be broken either in a hidden or the visible sector. However
hidden sector models suffer from several naturalness problems and have
difficulties in producing an acceptably large gluino mass.
