Sixth and higher moments of L-functions are important and challenging problems in analytic number theory. In this talk, I will discuss my recent joint works with Xiannan Li, Kaisa Matom\"aki and Maksym Radziw\il\l on an asymptotic formula of the sixth and the eighth moment of Dirichlet L-functions averaged over primitive characters mod q over all moduli q \leq Q (and with a short average over critical line for the eighth moment). Unlike the previous works, we do not need to include an average on the critical line for the sixth moment, and we can obtain the eighth moment result without the Generalized Riemann Hypothesis.