We are concerned with concave programming or the convex maximization problem which has many applications and is known as NP-hard problem. In this talk, we servey several results in concave programming that have appeared in recent years. The proposed methods and algorithms for solving the problem are based on the global optimality conditions. We show that some of the results can be applied to the quasiconvex maximization problem and a nonconvex optimal control problem with a convex terminal objective functional. Also, applications of concave programming in industrial and engineering problems will be discussed.