We report the construction of large new classes of models which break
supersymmetry dynamically. We then turn to model building. Two of the
principal obstacles to constructing simple models of dynamical supersy
mmetry breaking are the appearance of Fayet-Iliopoulos D terms and dif
ficulties in generating a mu term for the Higgs fields. Among the new
models are examples in which symmetries prevent the appearance of Faye
t-Iliopoulos terms. A gauge singlet field, which may play a role in ex
plaining the hierarchy in quark and lepton parameters, can generate a
suitable mu term. The result is a comparatively simple model, with a l
ow energy structure similar to that of the MSSM, but with far fewer ar
bitrary parameters. We begin the study of the phenomenology of these m
odels.