On Hecke eigenvalues of Maass cusp forms

For a Hecke-Maass newform F of level N and with pth Hecke eigenvalue a(p) where p is a prime, the generalized Ramanujan conjecture
asserts that a(p) is bounded by 2 in the absolute value for ( p, N) = 1. In this talk we will survey the recent results and developments
centered on this intriguing problem.