First proposed in 1971, the Cancellation Problem asks whether A[X_1,...,X_n] isomorphic to B[Y_1,...,Y_n] for rings A and B implies that A is isomorphic to B. In this talk we discuss a counterexample to the Cancellation Problem, a variant of the problem which holds, and a couple of modern results in the same genre. Speaker(s): Havi Ellers (University of Michigan, Ann Arbor)