This presentation will discuss stochastic control from a Model Predictive Control (MPC) perspective, focusing on the extension of some key MPC ingredients to linear systems subject to stochastic parametric uncertainties. We will first show how properties of the Kronecker product can be exploited to derive deterministic recursions for the covariance dynamics. Within a tube-based framework, such recursions provide a basis for uncertainty propagation and constitute an important step toward tractable chance- constraint tightening. We will then address the design of reduced-size suJicient conditions for stabilizing the covariance dynamics, with an emphasis on the trade-oJ between computational tractability and conservatism. The presentation will subsequently establish the connection between covariance stability and the classical notion of mean-square stability for stochastic systems. In particular, equivalent spectral conditions will be discussed, providing a counterpart to the classical Schur-stability characterization of deterministic linear systems. Finally, the talk will outline some remaining challenges and ongoing research directions.