A brief literature survey on bilevel optimization has been efficiently carried out in this paper. Bilevel optimization is a sequential process moving hierarchically from one level to another level problem. Numerous applications of bilevel programming can be seen in real world. Different aspects of bilevel problems comprising of mixed integer programming along with their solution techniques have been analyzed. The authors have scrutinized bilevel problems in which either lower level problem is convex or they have integral constraints. Mixed integer nonlinear bilevel problems are also examined in the paper. Further, bilinear terms in pricing or interdiction models leading to non-convex problems are also studied. A classification of interdiction problems based on the structures of the encompassed lower-level problems is also provided. A discussion on Stackelberg games involving linear constraints and bilinear objective functions at both the levels is also conducted in the paper. Various methods for solving bilevel programming problems consisting of linear as well as mixed nonlinear objective functions and to obtain its optimal solution are studied, namely, branch-and-bound method, branch-and-cut method, decomposition principle, cutting planes, \(K\)th best algorithm, to name a few. Distinct algorithmic and computational techniques are discussed in the paper which will be beneficial to the researchers working in this field. This paper has provided the researchers with all the prospects required for research in bilevel optimization.