n this talk, we present some of our recent work on stochastic Kolmogorov systems. The motivation stems from dealing with important issues of ecological and biological systems. Focusing on environmental noise, we aim to address such fundamental questions: "what are the minimal conditions needed for long-term persistence of a population, or long-term coexistence of interacting species". [The talk reports some of our joint work with D.H. Nguyen and N.N Nguyen, and also the work with N.T. Dieu, N.H. Du, among others.]