In this chapter, we discuss inventory control in a stochastic setting. We first introduce the Newsvendor problem, which is the simplest possible stochastic inventory system that can be conceived. Then we survey service level constraints and penalty cost schemes that can be adopted for modelling stochastic inventory systems. Next, we show how to model and simulate a stochastic inventory system running costs. Equipped with these notions, we extend the Newsvendor problem to a multi-period setting. Central to stochastic inventory theory is the notion of control policy. A control policy is a rule that establishes when inventory should be reviewed and orders issued, and how large an order should be. The rest of this chapter is devoted to presenting a range of control policies that are commonly adopted in inventory control and that can be used to control a number of well-known inventory systems.