In this paper we study the bilevel optimization problem, with special emphasis on the linear bilevel optimization problem where we assume that the functions on both levels are affine. Bilevel optimization problems have another (parametric) optimization problem as part of the constraints. For the linear bilevel optimization problems, properties and optimal solutions based on geometric interpretation are given. The existence of optimal solutions is studied, and using Karush-Kuhn-Tucker optimality conditions for the lower level problem, Karush- Kuhn-Tucker optimality conditions for the linear bilevel optimization problem are obtained. Algorithms for solving a given problem are given and the question of searching for a global optimal solution is raised. Without the assumptions of the affinity of the functions at both levels, a more general model of bilevel optimization is arrived at. Necessary and suficient optimality conditions are given as well as an algorithm for calculating the Clarke stationary point as the optimal solution to the problem. At the end of this paper, various applications of bilevel optimization in the real world are listed, which have had a strong impact on the growth of research on this optimization problem.