Semi-infinite optimization in its general form has recently attracted a lot of attention, not only because of its surprising structural aspects, but also due to the large number of applications which can be formulated as general semi-infinite programs. This is the first book which exploits the bilevel structure of semi-infinite programming systematically. It highlights topological and structural aspects of general semi-infinite programming, formulates powerful optimality conditions, and gives a conceptually new bilevel solution method. The book is addressed to graduate students and researchers who work in the fields of optimization and operations research. Notions which are necessary for understanding the material but which are not part of the standard university curriculum are briefly explained. After an introduction with some historical background in Chapter 1, the appearance of standard and general semi-infinite programming problems is motivated and illustrated by a number of problems from engineering and economics in Chapter 2. These include (reverse) Chebyshev approximation, minimax problems, robust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming. Chapter 3 is devoted to a thorough understanding of the topological structure of the feasible set in general semi-infinite programming. As the key for the treatment of these problems turns out to be a reformulation of the semi-infinite as a nonsmooth problem, Chapter 4 presents a framework for the construction of optimality conditions where only estimates of upper and lower directional derivatives of the data functions enter. A combination of these results with various explicit descriptions of linearization cones under different structural assumptions leads to powerful optimality conditions. Chapter 5 introduces a conceptually new solution method for general semi-infinite programs. In fact, after a reformulation as a Stackelberg game and then as a mathematical program with complementarity constraints, instead of the original problem the resulting MPCC is solved. For the proposed regularization procedure several convergence results are given. A number of numerical examples illustrate the performance of the proposed method in Chapter 6. Open questions and possible routes to further research conclude the book in Chapter 7.