Summary: The concept of weak algebraic hyperstructures or \(H_v\)-structures constitutes a generalization of the well-known algebraic hyperstructures (semihypergroup, hypergroup and so on). The overall aim of this paper is to present an introduction to some of the results, methods and ideas about chemical examples of weak algebraic hyperstructures. In this paper, after an introduction of basic definitions and results about weak algebraic hyperstructures, we review: {\parindent=0.6 cm \begin{itemize}\item[(1)] weak algebraic hyperstructures associated with chain reactions, \item[(2)] weak algebraic hyperstructures associated with dismutation reactions, \item[(3)] weak algebraic hyperstructures associated with redox reactions. \end{itemize}}