This Tutorial will discuss the motivation, benefits, and challenges of photonic switching in data centers and cover prospects of future data centers involving emerging new technologies and cross-layer solutions. The primary motivation for considering photonic switching in data centers rises from the need for energy-efficient and scalable intra-data center networks to meet rapid increases in data traffic driven by emerging applications, including machine learning. The data traffic inside the data centers (East-West traffic) is typically significantly greater than that of the traffic coming in and out of the data centers (North-South traffic) (Benson <i>et al.</i> 2010). To accommodate such traffic, today's large-scale data centers employ cascaded stages of many power-hungry electronic packet switches interconnected across the data center network in fixed hierarchical communication topologies. These electronic switches add significant latency and energy consumption while limiting the communication bandwidth. On the other hand, photonic switches can, in principle, support interconnections at very high data rates on many parallel wavelengths while keeping their energy consumption nearly independent of the switch port bandwidth. Numerous research papers have predicted significant benefits in scalability, throughput, and power efficiency from deploying photonic switches in data centers. However, photonic switching is not yet widely deployed in commercial warehouse-scale data centers at the time of writing this Tutorial due to significant challenges. They are related to 1) cross-layer issues involving control and management planes together with data integrity during switching, 2) scalability to >5000 racks (>a quarter-million servers), 3) performance monitoring required for reliable operation, 4) currently existing standards allowing limited power margin (3 dB), and 5) other practical (technology-dependent) issues relating to polarization sensitivity, temperature sensitivity, cost, etc. In telecom, commercial deployments of reconfigurable optical add-drop multiplexers (ROADMs) (Lightwave, 2003)–(Perrin, 2015) also had faced similar challenges and took place nearly ten years after the first research network testbed demonstrations in 1997 (Garrett, 2015) with fully implemented network control and management planes. In data centers, the challenges are far more significant due to the scale of the network and the dynamicity of the traffic. We will discuss possible solutions for future data centers involving cross-layer methods, new topologies, and innovative photonic switching technologies. In particular, the Tutorial broadly surveys state-of-the-art photonic switching technologies, architectures, and experimental results, and further covers the details of arrayed-waveguide-grating-router-based switch fabrics offering hybrid switching methods with distributed control planes towards scalable data center networking.