A Survey of Recent Progress on Non-Abelian Tensor Squares of Groups

We discuss some of the progress that has occurred since the survey article “Non- abelian tensor products of groups: the commutator connection” by L.C. Kappe appeared in the Proceedings of Groups St Andrews 1997 in Bath, with a particular emphasis on non-abelian tensor squares of groups. We survey methods for comput- ing non-abelian tensor squares, results that support such calculations, and recent general structure results.