One of the major challenges encountered in the design of data-driven algorithms for complex supply chain systems lies in the fact that observed data and the operational policies being implemented are inextricably linked and dependent. In this colloquium, I will present my recent works on the design of efficient learning algorithms for supply chain problems that address this issue. I will focus on two fundamental yet challenging stochastic inventory control problems: the inventory system with perishable products and the lost-sales inventory system with positive lead times. The decision maker is assumed to have no information about the underlying demand distribution a priori and can only observe past realized sales (censored demand) data to optimize the system's performance on the fly. For each problem, we design a non-parametric learning algorithm that can converge to the optimal base-stock policy with a provably tight regret rate. The design and analysis of these algorithms overcome the limitations of standard data-driven optimization algorithms, that result from complex system dynamics, inventory constraints, and prolonged impact on decision-making.