Non-Hermitian systems exhibit rich physical phenomena that open the door to qualitatively new forms of control. In this talk, I will introduce our recent work on topological and nonreciprocal dynamics in a non-Hermitian optomechanical system. Specifically, we realized topological energy transfer between nearly degenerate modes by adiabatically encircling an exceptional point (a singularity of the complex spectrum). We also demonstrated that this energy transfer is non-reciprocal: a given topological operation can only transfer energy in one direction. We have extended the topological and nonreciprocal dynamics to highly non-degenerate modes by exploiting a generic form of nonlinearity, which should allow these effects to be exploited in a very wide range of physical systems. In addition, we realized nonreciprocal dynamics by optomechanical interference.