Nonlinear dynamical systems arising in biological, physical and chemical sciences are often subject to random influences, which are also known as noise. Stochastic differential equations are appropriate models for some of these systems. The noise in these stochastic differential equations may be Gaussian or non-Gaussian in nature. Non-Gaussianity of the noise manifests as nonlocality at some macroscopic level. In addition, randomness may have delicate, or even profound, impact on the overall evolution of dynamical systems. The speaker will present an overview of some available theoretical and numerical techniques for analyzing stochastic dynamical systems, especially escape probability, mean exit time, invariant manifolds, bifurcation and quantifying the impact of uncertainty. The differences in dynamics under Gaussian and non-Gaussian noises are highlighted, theoretically or numerically.