n this talk, I will explore the conjectural link between random matrix theory and moments of L-functions. In particular, I will discuss the moments of the Riemann zeta-function and of the characteristic polynomials of random unitary matrices. I will then introduce a generalization, namely the moments of moments, along with their applications to extreme values and associated conjectures of Fyodorov and Keating. After discussing the recent results related to these conjectures, I will finish by looking at some recent results that give an analytic proof of the asymptotic of the symplectic and orthogonal moments of moments for characteristic polynomials and applications to the moments of moments of L-functions. This is joint work with Chris Best.