Adopting the physicist point of view and pursuing a predictive modeling approach raise immediately the following questions: How do we describe a disperse two-phase flow? And what is the structure of the governing equations retained to capture the characteristics of the disperse two-phase flows we wish to simulate? To answer these questions, this chapter provides an account of the governing equations that are either used or referred to in this book. It is thus written as an introduction for readers unfamiliar with the main equations, like the Navier-Stokes equations for the dynamics of fluids and the particle equations of motion.