Bent functions correspond to relative difference sets in the groups $Z^n_2\times Z_2$ respectively $Z^n_2 \times Z_2m$ . Being highly nonlinear, Boolean bent functions have application in cryptography. Whereas there are many constructions of Boolean bent functions, bent functions from $Z^n_2$ to $Z_2m$ seem to be quite rare. Recently a lot of research has been performed on generalized bent (gbent) functions, which are functions from $Z^n_2$ to $Z_2m$ satisfying the weaker condition that $H_f(1,u)$ has absolute value $2^{n/2}$ for every $u \in Z^n_2$. In this talk, the main results on gbent functions and bent functions from $Z^n_2$ to $Z_2m$ are summarized, and some open questions are discussed.