This paper is written against the backdrop of the growing interest in enabling intelligent services directly on resource-constrained devices due to the convergence of artificial intelligence and edge computing. Existing deep learning models require significant computing resources and centralized data management, and the resulting latency, bandwidth consumption, and privacy concerns expose the critical limitations of the cloud-centric paradigm. In this paper, we provide a comprehensive overview of Edge Intelligence (EdgeSNNs) based on spiking neural networks (SNNs) that mimic the dynamics of biological neurons to achieve low-power event-based computing. We present a systematic taxonomy of EdgeSNNs, including neuron models, learning algorithms, and supporting hardware platforms, and deeply discuss three representative practical considerations: on-device inference using lightweight SNN models, resource-aware learning and updating under abnormal data conditions, and security and privacy concerns. We also highlight the limitations of evaluating EdgeSNNs on existing hardware and introduce a dual-tracking benchmarking strategy to support fair comparison and hardware-aware optimization. This study aims to bridge the gap between brain-inspired learning and real-world edge deployments, and provide insights into current progress, open challenges, and future research directions. This paper is the first dedicated and comprehensive survey of EdgeSNN, and serves as an essential reference for researchers and practitioners working at the intersection of neuromorphic computing and edge intelligence.