By a closure space we will mean a pair* (A,$\backslash$( $\backslash$mathscr C $\backslash$))*, in which *A* is a set and\ *$\backslash$( $\backslash$mathscr C $\backslash$)* a set of subsets of *A* closed under arbitrary intersections. The purpose of this paper is to initiate a development of descent theory of closure spaces, with our main results being: (a) characterization of descent morphisms of closure spaces; (b) in the category of finite closure spaces every descent morphism is an effective descent morphism; (c) every surjective closed map and every surjective open map of closure spaces is an effective descent morphism.