The class of strongly quasiconvex functions was introduced in the famous paper of B.T. Polyak in 1966. It is the natural extension of the class of strongly convex functions, its applications emcompasses different problems from mathematical sciences, economics and engineering among others and, furthermore, they are especially useful for algorithms purposes. In this talk, we present an overview on strongly quasiconvex functions from the open question regarding the existence of solutions for the minimization problem until its solution in 2022. As a consequence, we study properties for the proximity operator and its applications in proximal point algorithms and subgradient projection methods for studying nonsmooth strongly quasiconvex functions.