This article provides a brief theoretical review and description of curves that showed superior fitness: Logistic, Gompertz, Mixed Informational Source model, Bass model, multi-generation and multi-product diffusion models, and the one that combines the concepts of technical substitution and market competition. In order to choose an appropriate model and distinguish driving forces a survey of methods and mathematical models which were successfully used in empirical studies of diffusion of ICT services in economics has been made.