摘要：In this talk, I will first give a brief review of the propagation dynamics of evolution equations in a shifting environment. Then I will report our recent research on a large class of time and space heterogeneous reaction-diffusion equations. We obtain the leftward and rightward spreading speeds in terms of the shifting speed and the spreading speed of an associated limiting equation. We also establish the existence, uniqueness and nonexistence of the forced traveling wave, and further apply this result to obtain the existence of almost periodic traveling waves for nonautonomous SIS epidemic models.