In this paper, we develop stochastic dissipativity theory for nonlinear dynamical systems using basic input-output and state properties. Specifically, a stochastic version of dissipativity using both an input-output as well as a state dissipation inequality in expectation for controlled Markov diffusion processes is presented. The results are then used to derive extended Kalman–Yakubovich–Popov conditions for characterizing necessary and sufficient conditions for stochastic dissipativity of stochastic dynamical systems using two-times continuously differentiable storage functions. In addition, feedback interconnection stability in probability results for stochastic dynamical systems are developed thereby providing a generalization of the small gain and positivity theorems to stochastic systems.