The linear approximation that we have used so far in the study of collective effects can easily break down. Finite and non-negligible amplitudes are generally unavoidable, and often even desirable, in experimentally generated waves. Moreover, initially small wave amplitudes can grow as a result of an instability and quickly leave the linear regime. Various physical processes then become significant. Clearly, a description in terms of individual Fourier modes is generally no longer adequate, since couplings (convolution integrals) and nonlinear interactions occur. In addition, particles can become truly trapped in pronounced wave troughs (“particle trapping”). Furthermore, a large-amplitude wave alters key plasma parameters, such as local particle density, temperature, and so on. All these phenomena require extensive analysis. In this chapter, we focus on some important effects in coherent wave phenomena, where phase information is tracked deterministically. Later, in the context of laser-plasma interaction, we will refer back to parts of this chapter.