We briefly review the results concerning the minimization of quadratic functions subject to linear and/or separable convex constraints. We review the formulation of optimization problems, the existence and uniqueness of the solution, the specific forms of the KKT conditions, and the duality theory, including semicoercive problems. The choice of topics is sufficient for understanding the algorithms described in the rest of the book. The results are presented with arguments that exploit the specific structure of these problems.