Most standard theoretical approaches emphasize the role of deterministic density dependence in creating and maintaining equilibrium dynamics. At the same time, it is widely recognized that ecological processes are inherently stochastic, and that disturbances and variation in the environment and in the fates of individuals prevent many ecological systems from resting at their theoretical equilibrium. A developing body of stochastic ecological theory aims to bridge the gap between the deterministic tools of classical theory and the stochastic, non-equilibrial questions that real systems present to us. This chapter provides an overview of this developing theory, with an emphasis on approaches that confront the complex interplay between deterministic density dependence, and perturbations. Although intuition may suggest that stochasticity and transient phenomena should obscure ecological understanding, they can actually strengthen it when viewed through the appropriate lens, as illustrated in this chapter.