The rapid growth of Internet of Things (IoT) has led to the widespread deployment of smart IoT devices at wireless edge for collaborative machine learning tasks, ushering in a new era of edge learning. With a huge number of hardware-constrained IoT devices operating in resource-limited wireless networks, edge learning encounters substantial challenges, including communication and computation bottlenecks, device and data heterogeneity, security risks, privacy leakages, non-convex optimization, and complex wireless environments. To address these issues, this article explores a novel framework known as distributed swarm learning (DSL), which combines artificial intelligence and biological swarm intelligence in a holistic manner. By harnessing advanced signal processing and communications, DSL provides efficient solutions and robust tools for large-scale IoT at the edge of wireless networks.