The cyclic sieving phenomenon is a decade-old object in enumerative combinatorics introduced by Reiner, Stanton, and White related to counting the fixed-point set sizes associated with a finite cyclic group acting on a finite set. We will give examples of the CSP for combinatorial actions on Young tableaux, polygon dissections, and set partitions. We will see that, while the statement of the CSP is purely enumerative, the ``best" proofs of CSPs are algebraic and instances of the CSP can predict results in algebra and geometry.