The definitions of recursive and G-recursive functions will be recalled. Then some fundamental results and properties of these functions will be presented. Especially their relation to Baire classes and effective Baire classes will be considered. The connections between these notions and analog computations will be analysed. The meaning of a differential recursion, minimalization operator and infinite limits in the above context will be discussed. Also the place of hierarchies of real recursive functions in descriptive set theory will be studied.