We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems. Under assumptions that include, for example, iterated function systems, but that exclude stochastic differential equations, we demonstrate how random attractors can be seen as examples of Milnor attractors for a skew-product system.