Random matrices were introduced in physics by Wigner in the 50's in order to understand properties of the compound nucleus. This (parameter-free) model has known an astonishing success. Periodic orbit theory has provided a dynamical basis to understand this success, relating it to chaotic dynamics.
That there are close similarities between random matrices and properties of Riemann zeros was realized since the early 70's. More recently properties of the Riemann's zeta function have been studied with what has been learned in random matrices and in periodic orbit theory. Some robust and partly unexpected results have been derived, mostly heuristically. This has given rise to an active field of research, were theoretical physics and mathematics meet.
After giving the main ideas of this general framework, some recent developments and results will be discussed.