  In this thesis generalizations of matrix and eigenvalue models involving
supersymmetry are discussed. Following a brief review of the Hermitian one
matrix model, the c=-2 matrix model is considered. Built from a matrix valued
superfield this model displays supersymmetry on the matrix level. We stress the
emergence of a Nicolai-map of this model to a free Hermitian matrix model and
study its diagrammatic expansion in detail. Correlation functions for quartic
potentials on arbitrary genus are computed, reproducing the string
susceptibility of c=-2 Liouville theory in the scaling limit. The results may
be used to perform a counting of supersymmetric graphs.
  We then turn to the supereigenvalue model, today's only successful discrete
approach to 2d quantum supergravity. The model is constructed in a
superconformal field theory formulation by imposing the super-Virasoro
constraints. The complete solution of the model is given in the moment
description, allowing the calculation of the free energy and the multi-loop
correlators on arbitrary genus and for general potentials. The solution is
presented in the discrete case and in the double scaling limit. Explicit
results up to genus two are stated.
  Finally the supersymmetric generalization of the external field problem is
addressed. We state the discrete super-Miwa transformations of the
supereigenvalue model on the eigenvalue and matrix level. Properties of
external supereigenvalue models are discussed, although the model corresponding
to the ordinary supereigenvalue model could not be identified so far.
