Complex dynamical systems are often under random fluctuations. The noisy fluctuations may be Gaussian or non-Gaussian, which are modeled by Brownian motion or α-stable Levy motion, respectively. The speaker will overview recent advances in deterministic methods for stochastic dynamical systems, including mean exit time, escape probability, most probable transition trajectories, and extracting stochastic governing laws from noisy data. These methods involve nonlocal partial differential equations with singular integral operators.