This book is primarily a presentation of nonlinear energy stability results obtained in convection problems by means of an integral inequality technique we refer to as the energy method. While its use was originally based on the kinetic energy of the fluid motion, subsequent work has, for a variety of reasons, introduced variations of the classical energy. The new functionals have much in common with the Lyapunov method in partial differential equations and standard terminology in the literature would now appear to be generalized energy methods. In this book we shall describe many of the new generalizations and explain why such a generalization was deemed necessary. We shall also explain the physical relevance of the problem and indicate the usefulness of an energy technique in this context.