DescriptionWe expand upon the theory of random dynamical systems (RDS) of L. Arnold, developing a theory of random dynamical systems with inputs and outputs (RDSIO)—an abstract framework for the treatment of noise-driven systems subject to stochastic inputs and yielding random outputs. This development allows for one to study both autonomous RDS and proper RDSIO as the feedback interconnection of smaller random input/output modules. As “proof of concept,” we prove a small-gain theorem for autonomous RDS which can be realized as the feedback interconnection of monotone RDSI with monotone or anti-monotone outputs. This result gives sufficient conditions for autonomous RDS to possess unique, globally attracting equilibria—the RDS in question need not be itself monotone.