This is a systematic study of order-preserving (or monotone) random
dynamical systems which are generated by
cooperative random or stochastic differential equations.
Our main results concern the long-term behavior of these systems, in
particular the existence of equilibria and attractors and
a limit set trichotomy theorem.
Several applications (models of the control of the protein synthesis
in a cell, of gonorrhea
infection and of symbiotic interaction in a random environment)
are treated in detail.