The construction of morphological filters, i.e., morphological operators which are increasing and idempo- tent, is an important problem in mathematical morphology. In this paper it is described how one can construct openings and closings and other morphological filters by iteration. It turns out that a sort of order continuity is required to guarantee that iteration leads to idempotence. An important class of operators which yield morphological filters after iteration are the so-called pointwise monotone operators. In the last section the abstract theory is illustrated by a number of concrete examples.