The concept of a T-discrete object is a generalization of the notion of discrete spaces in concrete categories. In this paper. T-discrete objects are used to define discrete functors. Characterizations of discrete functors are given and their relation to other important functors are studied. A faithful functor T:A→Xis discrete iff the full subcategoryBofAconsisting of all T-discrete objects is (X-iso)-coreflective inA. It follows that the existence of bicoreflective subcategories is equivalent to the existence of suitable discrete functors. Finally, necessary and sufficient conditions are found such that for a given functor T:A→X, the full subcategoryBofAconsisting of all T-discreteA-objects is monocoreflective inA.