The dynamics of species’ densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include abiotic factors or non-focal species. These internal or external variables may fluctuate due to stochastic fluctuations in environmental conditions. The interplay between these variables and species densities can determine whether a particular population persists or goes extinct. I will present recent theorems for stochastic persistence and exclusion for stochastic ecological difference equations accounting for internal and external variables, and will illustrate their utility with applications to models of eco-evolutionary dynamics.