All populations experience stochastic uctuations in abiotic factors such as temperature, nutrient avail- ability, precipitation. This environmental stochasticity in conjunction with biotic interactions can facilitate or disrupt persistence. One approach to examining the interplay between these deterministic and stochastic forces is the construction and analysis of stochastic dierence equations and stochastic dierential equations. Many theoretical biologists are interested in whether the models are stochastically bounded and persis- tent. Stochastic boundedness asserts that asymptotically the population process tends to remain in compact sets. In contrast, stochastic persistence requires that the population process tends to be epelled" by some "extinction set". Here, I will review recent results on both of these proprieties are reviewed for models of multi-species interactions and spatially-structured populations. Basic results about random products of matrices, Lyapunov exponents, stationary distributions, and small-noise approximations will be discussed. Applications include bet-hedging, coexistence via the storage eect, and evolutionary games in stochastic environments.