This book presents numerous mathematical methods used in the study of initial and boundary problems for Bingham fluids and rate dependent viscoplasticity. Existence and uniqueness results are presented and the behavior of the solutions with respect to the data is studied in detail. For many problems, the numerical approximation of the solution is also given and numerical results are presented. Elliptic variational inequalities, convex functions, monotone operators, semigroups of operators, and nonlinear evolution equations are used as mathematical instruments. Mathematical results are carefully interpreted from a mechanical point of view, allowing the author to present a theory to deal with numerical results and their possible practical applications to industrial and technological innovations. This book will appeal to mathematicians, physicists, engineers, and students interested in this topic of increasing importance.