Lyapunov exponents play an important role in the study of the behavior of dynamical systems. They measure the average rate of separation of orbits starting from nearby initial points. They are used to describe the local stability of orbits and chaotic behavior of systems. Multiplicative Ergodic Theorem provides the theoretical foundation of Lyapunov exponents, which gives the fundamental information of Lyapunov Exponents and their associates invariant subspaces. In this talk, I will report the work on Multiplicative Ergodic Theorem (with Kening Lu), which is applicable to infinite dimensional random dynamical systems in a separable Banach space. The system could be generated by, for example, random partial differential equations.