What sort of algebraic objects do we get if, in place of a standard binary operation on a set, we consider an operation that is multi-valued? A hypergroup is a set with a binary operation into its set of nonempty subsets, satisfying certain axioms (that are similar to standard group axioms/properties). A hyperring is a "ring" but where the underlying group is a hypergroup. One could similarly define a whole world of hyperstructures. We give basic definitions, examples, motivation and talk about some algebraic constructions that we can do with hyperstructures. This is an expository talk.