Description The theory is illustrated with numerous examples of *-algebras. The examples, in particular, include *-algebras with two self-adjoint generators that satisfy a quadratic or a more general relation, *-algebras with three and four generators, *-algebras that arise from one and many-dimensional discrete dynamical systems, Wick *-algebras, various *-wild algebras. This review is intended for graduate students and researchers who specialize in this area of mathematics