In work in the mid-90's, John Stembridge noted that several combinatorial statistic generating functions carried enumerative information when the variable was set to $-1$. He dubbed this the "$q=-1$ phenomenon. In joint work with Vic Reiner and Dennis Stanton, we have noted that Stembridge's phenomenon generalizes to when $q$ is an appropriate root of unity. We called this the "cyclic sieving phenomenon." I will describe several instances of this phenomenon and some open problems.