The compositional module in the MATLAB Reservoir Simulation Toolbox (MRST) implements two different formulations of a three-phase compositional system that consists of a pair of multicomponent phases and an optional immisicible phase. In petroleum engineering, the aqueous phase is taken to be immiscible and the hydrocarbon liquid and vapor phases are governed by an equation of state (EoS). The overall composition formulation uses pressure and overall mole fractions as primary variables, whereas the natural variable formulation relies on solving for phase mole fractions and phase saturations simultaneously. Thermodynamic behavior is modeled using $K$-values or a (standard) cubic EoS. In the chapter, you will learn about the model equations, choice of primary variables, and numerical strategies for solving the thermodynamic problem, alone or coupled to the flow equations. We discuss details of the implementation, which builds upon the object-oriented, automatic differentiation (AD-OO) framework and utilizes state functions and generic model classes for increased modularity. We also present a few relatively simple simulation examples to illustrate typical behavior and teach you how to set up simulation cases yourself.