Schur's Lemma is one of the fundamental results of the theory of simple modules. It states that if M is a simple right module over a ring R, then its endomorphism ring is a division ring. However, the converse of Schur's Lemma is, in general, not true for either commutative or noncommutative rings. Nevertheless, the converse of Schur's Lemma does hold for certain kinds of rings. We will describe some of those rings in both the commutative and the noncommutative cases.