Representation of functions by series and classes $\varphi(L)$

In the paper we give a survey of results concerning the problems of representing functions by series in various systems, and of the uniqueness of such a representation. The account covers older results as well as those of recent years due to several authors. Much attention is also paid to questions of the validity of the Weierstrass theorem and of representing functions in the classes $\varphi(L)$.