In this talk I will give a survey on the notion of cohomology in the theory of random dynamical systems, which have its origin in homological algebra. A classical result is that the Lyapunov spectrum and random attractors are invariant under a Lyapunov cohomology. Cohomologies therefore help to define the structural stability of stochastic systems and to study the bifurcation phenomena. For applications, I will present our new results on random attractors for rough differential equations using the cohomology method.