Abstract: This paper summarized some recent advances in the propagation of high-power lasers passing through amplifiers.Starting from Frantz-Nodvik equetion,using pulse-sequence and slab-loss and gain models,high-power lasers propagating through scingle-and multi-pass amplifiers have been studied in detail,which is suitable,in particular,for the can of nelatively large losses,and can be extended to dealing with the inverse problem of amplifiers by means of the succersive iferation computing method.