Historically, the Cancellation Problem arises as the problem of

uniqueness of coefficient rings in commutative algebra. The question at that time

was to decide if the existence of an isomorphism between two polynomial rings A[t]

and B[t] in one variable t always implies that the coefficient rings A and B

are isomorphic. In this talk, I will discuss geometric interpretations and

generalizations of this question and survey the known positive results and

counter-examples.