The current talk is concerned with transition fronts of nonlocal dispersal evolution equations in heterogeneous media. As it is known, solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal dispersal evolution equations. In the current talk, I will first present some general criteria concerning space regularity of transition fronts in nonlocal dispersal evolution equations with a large class of nonlinearities. I will the discuss the existence, uniqueness, and stability of transition fronts on nonlocal dispersal evolution equations with monostable, bistable, and ignition type nonlinearities in time heterogeneous media. This talk is based on my joint works with Zhongwei Shen.