New aspects of N=2 theories

We review some recent observations in theories with eight supercharges. We point out that such theories can be generalized by starting from the equations of motion rather than from an action. We show that vector multiplets constructed in such a way can have more general Fayet-Iliopoulos terms and that the scalar fields of hypermultiplets can be coordinate functions on more general target spaces. Although our discussion holds in five dimensions, the results can easily be extended to other dimensions.