In this paper, I have gathered together some results I have proved for the Carleson measures in the unit disc $|z|<1$ in terms of a new characteristic function. In the case of meromorphic functions, the introduced characteristic function becomes the Nevanlinna characteristic function in the form of Ahlfors--Shimizu. The new characteristic function is used to obtain the necessary and sufficient conditions for a meromorphic function to belong to the class $BC$ of functions with the bounded Nevanlinna characteristic, to the class $UBC$ of functions with the uniformly bounded Nevanlinna characteristic, and for a holomorphic function to belong to the Hardy spaces $H^p$, $0<p<\infty$, to the hyperbolic Hardy classes $H^p_h$, $0<p<\infty$, to the classes $BMO$ and $BMOA$.