In this chapter, we present general methods for modeling waves in plasmas with larger amplitudes, which we then refer to as nonlinear. In principle, we would have to do this separately for each individual wave type. However, we illustrate common methods using only a few types (ion-acoustic oscillations, Langmuir oscillations, and drift vortices), with the expectation that once the fundamental procedure has been demonstrated for some modes, transferring and generalizing it to other modes should not be too difficult. Central to this, of course, is whether the nonlinear oscillatory states thus found are also observable, i.e., stable from a mathematical standpoint. Among other things, we present exact solutions using the inverse scattering method. While most of the chapter focuses on coherent states, we address turbulent states at the end. However, this is done without any claim to a comprehensive presentation of the important but also extremely challenging current approaches to turbulence.