With the proliferation of distributed edge computing resources, the 6G mobile network will evolve into a network for connected intelligence. Along this line, the proposal to incorporate federated learning into the mobile edge has gained considerable interest in recent years. However, the deployment of federated learning faces substantial challenges as massive resource-limited IoT devices can hardly support on-device model training. This leads to the emergence of split learning (SL) which enables servers to handle the major training workload while still enhancing data privacy. In this article, we offer a brief overview of key advancements in SL and articulate its seamless integration with wireless edge networks. We begin by illustrating the tailored 6G architecture to support edge SL. Then, we examine the critical design issues for edge SL, including innovative resource-efficient learning frameworks and resource management strategies under a single edge server. Additionally, we expand the scope to multi-edge scenarios, exploring multi-edge collaboration and mobility management from a networking perspective. Finally, we discuss open problems for edge SL, including convergence analysis, asynchronous SL and U-shaped SL.