In this tutorial, we will survey the rich body of literature on methodical aspects, mathematical foundations and empirical case studies of synthetic controls. We will provide guidance for empirical practice, with special emphasis on feasibility and data requirements, and characterize the practical settings where synthetic controls may be useful and those where they may fail. We will describe empirical case studies from policy evaluation, retail, and sports. Moreover, we will discuss mathematical connections of synthetic controls to matrix and tensor estimation, high dimensional regression, and time series analysis. Finally, we will discuss how synthetic controls are likely to be instrumental in the next wave of development in reinforcement learning using observational data.