  We provide a survey of results concerning both the direct and inverse
problems to the Cauchy-Davenport theorem and Erdos-Heilbronn problem in
Additive Combinatorics. We formulate an open conjecture concerning the inverse
Erdos-Heilbronn problem in nonabelian groups. We extend an inverse to the Dias
da Silva-Hamidoune Theorem to Z/nZ where n is composite, and we generalize this
result into nonabelian groups.
