Various geometric (e.g. Poisson, Courant, generalized complex) structures may be rephrased in terms of graded symplectic manifolds endowed with functions satisfying certain equations. From the latter point of view the most general reduction is just that of graded presymplectic submanifolds compatible with the given functions. By translating this back to the language of ordinary differential geometry, we recover all the known reduction procedures plus new ones. For example, in the Poisson world we get various generalizations of the Marsden-Ratiu reduction. This is based on joint work with Bursztyn, Mehta, and Zambon.