In this talks, we discuss the dynamics of a special type of transcendental meromorphic functions called shift-pseudoperiodic functions. We first show that the Fatou set of such functions is invariant under certain translations. Next, we show that these functions can never have Baker wandering domains. Some non-existence criteria of Herman rings for such functions will be discussed. A detailed discussion on completely invariant Fatou components will be considered in the presentation.\r\nFinally, a brief account of the dynamics of semigroups generated by shift-pseudoperiodic entire functions is presented.
