This book considers some typical nonlinear dynamical systems with various random noises. It presents the reviews about nonlinear and stochastic dynamics, with some historic background and recent developments. Theoretical and numerical approaches will be carried out for some typical nonlinear dynamical systems. It is written with a wide audience in mind and presents basic techniques for readers to learn and investigate stochastic dynamics. This book serves as a reference book or textbook for students and researchers in mathematics, engineering, physics, chemistry, biology and social sciences, and other professionals who are interested in the subject and help them quickly get into the field and ready for studies.