We provide a taxonomy of dynamical supersymmetry-breaking theories, an
d discuss the cosmological implications of the various types of models
. Models in which supersymmetry breaking is produced by chiral superfi
elds which only have interactions of gravitational strength (e.g., str
ing theory moduli) are inconsistent with standard big bang nucleosynth
esis unless the gravitino mass is greater than similar to 3X10(4) GeV.
This problem cannot be solved by inflation. Models in which supersymm
etry is dynamically broken by renormalizable interactions in flat spac
e have no such cosmological problems. Supersymmetry can be broken eith
er in a hidden or the visible sector. However, hidden sector models su
ffer from several naturalness problems and have difficulties in produc
ing an acceptably large gluino mass.