With the proliferation of versatile Internet of Things (IoT) services, smart IoT devices are increasingly deployed at the edge of wireless networks to perform collaborative machine learning tasks using locally collected data, giving rise to the edge learning paradigm. Due to device restrictions and resource constraints, edge learning among massive IoT devices faces major technical challenges caused by the communication bottleneck, data and device heterogeneity, non-convex optimization, privacy and security concerns, and dynamic environments. To overcome these challenges, this article studies a new framework of distributed swarm learning (DSL) through a holistic integration of artificial intelligence and biological swarm intelligence. Leveraging efficient and robust signal processing and communication techniques, DSL contributes to novel tools for learning and optimization tailored for real-time operations of large-scale IoT in edge wireless environments, which will benefit a wide range of edge IoT applications.