The main aim of this paper is to provide a brief review of the state-of-the-art studies in nonsmooth semi-infinite programming problems. In particular, we give an overview of the different nonsmooth semi-infinite optimization problems and their related applications. Some necessary and sufficient optimality conditions for a nonsmooth semi-infinite multiobjective programming problem when the objective and constraint functions are locally Lipschitz are stated. We also focus on such optimality conditions without the locally Lipschitz assumption.