We will give an overview of wave kinetic theory, focusing on the one-dimensional MMT system. This system, which encompasses the 1D NLS, is unique within the context of kinetic theory as the kinetic equation is trivial for some dispersion relations. We begin with some history of kinetic equations and a discussion of recent progress on their derivations. Then, we will focus on the main techniques of such derivations. We will finish with a discussion of a replacement theory when the kinetic equation is trivial. This talk is based on recent work put up on the arxiv, https://arxiv.org/abs/2408.13693.