Polynomial identity testing (PIT) is the problem of deciding if two multivariate polynomials are the same. In this talk, I will give an introduction to PIT and illustrate how it may be leveraged to solve combinatorial decision problems. In particular, we will see how PIT may be used to solve the Schubert vanishing problem. Lastly we will discuss how these ideas extend towards counting problems. This includes joint work with Igor Pak.