Supersymmetric Yang-Mills theories from domain wall fermions

We present work in progress on employing domain wall fermions to simulate N = 1 supersymmetric Yang-Mills theories on the lattice in d = 4 and d = 3 d imensions. The geometrical nature of domain wall fermions gives simple insi ghts into how to construct these theories. We also discuss the obstacles as sociated with simulating the N = 2 theory in d = 4.