  We give a survey and unified treatment of functional integral representations
for both simple random walk and some self-avoiding walk models, including
models with strict self-avoidance, with weak self-avoidance, and a model of
walks and loops. Our representation for the strictly self-avoiding walk is new.
The representations have recently been used as the point of departure for
rigorous renormalization group analyses of self-avoiding walk models in
dimension 4. For the models without loops, the integral representations involve
fermions, and we also provide an introduction to fermionic integrals. The
fermionic integrals are in terms of anti-commuting Grassmann variables, which
can be conveniently interpreted as differential forms.
