In 1972, S. Bloch asked for a construction of a general semiregularity mapfor algebraic cycles. In this talk such a map will be constructed. The existence of a semiregularity map has well known applications to the structure of theHilbert scheme and to the infinitesimal Hodge conjecture. We do not only generalizethese results considerably but also give new applications to deformations of modulesthat encompass, e.g., results of Artamkin and Mukai.