The Lengyel–Epstein model of the chlorite iodide malonic acid (CIMA) chemical reaction has received considerable attention from the research community particularly because it represented the first ever realization of the revolutionary work presented by Alan Turing in 1952. In this chapter, we review the most relevant and important studies related to the Lengyel–Epstein system. We restrict our review to those studies containing novel findings related to the dynamics of the model. In order to assist the user in linking things together and comprehending the work presented, we have made it our purpose in this chapter to start with a summary of the necessary theory behind each of the findings. The literature is classified into sections examining different characteristics of the model including the local and global asymptotic stability, the existence of Turing patterns, and the Hopf–bifurcation. In addition, we list a number of modifications made to the original system with particular focus being paid to the CDIMA reaction model, which adds a new term denoting the illumination intensity referring to the photosensitive nature of the reaction. Some simple numerical examples are also presented to illustrate the behavior of the model and the types of patterns that may arise.