Real recursive functions are defined similarly to the classical case, with the difference that we take functions defined on the reals. Although apparently different, several connections between these two approaches are known to exist. In this talk, we further extend those connections. In particular, we define new classes of real recursive functions and relate them with the classes of primitive recursive, recursive and partial recursive functions. We also present an analog of the Arithmetical Hierarchy for the real case and establish connections between the two. Some considerations on the limitations of this kind of connections are also taken in account. Finally, we establish links between real recursive functions and analog circuits.