I will address the problem of which *-algebras can be faithfully represented as algebras of operators acting on Hilbert spaces. We discuss an analogue of the Choi-Effros theorem characterizing abstract operator systems valid for *-algebras. We introduce Groebner basis methods to define a class of *-algebras given by generators and relations. Algebras from this class have an analogue of regular representation of group algebras and can be represented by unbounded operators. This class generalizes monomial *-algebras studied by C. Lance and P.Tapper as well as the class of *-doubles. We also discuss some applications to operator algebras and some open questions.