Abstract: In this talk, we study stochastic Kolmogorov systems. The motivation stems from the need for characterizing long-term behavior in many ecological, biological, and environmental systems. The survival of an organism is affected by time and space dependent biotic (competition for resources, predator-prey interactions) and abiotic (light, precipitation, availability of resources) factors. Concentrating on environmental noise, the fundamental issues that need to be addressed are: What are the minimal conditions for long-term persistence of a population, or for the long-term coexistence of interacting species? We present some of our recent work in such stochastic dynamic systems.