I am working on algebraic hyperstructures from 1995. During the last twenty years, I together with my students and co-authors studied and developed the theory of algebraic hyperstructures in many directions. In particular, we tried to find real examples of hyperstructures in nature. In this paper we review some parts of these works such as (1) Fundamental relations on hyperstructures; (2) Fuzzy sets and hyperstructures; (3) Rough sets and hyperstructures; (4) Topology and hyperstructures; (5) Number theory and hyperstructures; (6) n-ary hypergroups and there extension to hyperrings and hypermodules; (7) Applications of hyperstructures in biology, physics and chemistry.