The chapter introduces the concept of random dynamical systems, which combine ideas from probability theory and dynamical systems to model physical processes. It discusses the limitations of deterministic models due to inaccuracies in initial conditions and external noise, leading to the need for incorporating randomness into models. The chapter covers various models of random perturbations, including random noise, random maps, and random flows, and presents the abstract framework of skew-product maps. It also explores the multiplicative ergodic theorem for random dynamical systems, which generalizes the classical theorem for deterministic systems. The chapter further discusses the stochastic stability of physical measures, emphasizing the importance of understanding the asymptotic behavior of orbits under small random changes. Finally, it delves into the characterization of measures satisfying the entropy formula and the construction of physical measures as zero-noise limits, highlighting the significance of these results in both random and non-random dynamical systems.The chapter introduces the concept of random dynamical systems, which combine ideas from probability theory and dynamical systems to model physical processes. It discusses the limitations of deterministic models due to inaccuracies in initial conditions and external noise, leading to the need for incorporating randomness into models. The chapter covers various models of random perturbations, including random noise, random maps, and random flows, and presents the abstract framework of skew-product maps. It also explores the multiplicative ergodic theorem for random dynamical systems, which generalizes the classical theorem for deterministic systems. The chapter further discusses the stochastic stability of physical measures, emphasizing the importance of understanding the asymptotic behavior of orbits under small random changes. Finally, it delves into the characterization of measures satisfying the entropy formula and the construction of physical measures as zero-noise limits, highlighting the significance of these results in both random and non-random dynamical systems.