Mixed-integer nonlinear optimization (MINLO) models contain both integer decision variables and nonlinear functions in the objective or constraints. We first provide some example applications for this class of optimization model. Techniques for solving MINLO problems when the nonlinear functions are convex are briefly discussed. We then present the spatial branch-and-bound algorithmic framework for solving MINLO problems that contain nonconvex functions, focusing in particular on methods for constructing convex relaxations and partitioning the feasible region. Specialized techniques for constructing relaxations in the case of (nonconvex) quadratic constraints will be presented.