We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on ${ \cal N}=1$ and ${ \cal N}=4$ super Yang-Mills in four dimensions. Brief reviews of the corresponding lattice formalisms are given and current results are presented and discussed. We conclude with a summary of the main aspects of current work and prospects for the future.
Categories: hep-lat hep-th