We review the basic equations describing the microscopic diffusion of elements in stars. We describe the two formalisms commonly used to describe a stellar plasma, i.e., the Chapman-Enskog method and the Burgers equations. We point out the underlying assumptions about the physical state of the plasma itself. We briefly describe the different approximations which are often used to solve these equations, and discuss their validity. One of the major problems lies in the calculation of the collision integrals, and we discuss the different approaches to solving these integrals, emphasizing on their domain of validity.