Ridesharing systems are increasingly important components of the transportation infrastructure, and understanding how to design them efficiently, and how they affect society at large, is one of the pressing problems of the day. Moreover, from an academic perspective, ridesharing platforms are amazing laboratories for real-time algorithms, presenting challenges in large-scale learning, real-time stochastic control and market design. In this talk, we will go over the basic structure of a ridesharing system, summarize the state-of-the-art in theoretical models and algorithms, and discuss the main open questions posed by these platforms.