  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 supersymmetry breaking are
the appearance of Fayet-Iliopoulos D terms and difficulties in generating a
$\mu$ term for the Higgs fields. Among the new models are examples in which
symmetries prevent the appearance of Fayet-Iliopoulos terms. A gauge singlet
field, that may play a role in explaining the hierarchy in quark and lepton
parameters, can generate a suitable $\mu$ term. The result is a comparatively
simple model, with a low energy structure similar to that of the MSSM, but with
far fewer arbitrary parameters. We begin the study of the phenomenology of
these models.
