Inspired by the biological nervous system, the concept of neuromorphic computing was introduced in the 1980s. It aims to mimic the structure and function of the biological brain to achieve more efficient and biologically plausible computation. As a representative model of neuromorphic computing, spiking neural networks (SNNs) have been widely employed in edge intelligence tasks with strict resource constraints due to their spike sparsity, event-driven operation, biological interpretability, and hardware compatibility. This study summarizes the edge deployment of SNNs. First, based on the principles of the SNN model itself, it discusses the energy-efficient computation of SNNs and their huge potential for edge deployment. Then, the currently common hardware implementation toolchain for SNNs is introduced, and a detailed summary and analysis of SNN deployment on various types of neuromorphic hardware platforms are provided. Finally, considering that hardware fault behavior has become an unavoidable issue in current research, an overview of fault and fault tolerance research during deploying SNNs at the edge is also presented. This study offers a comprehensive and systematic summary of recent advances in neuromorphic computing,ranging from software model principles to hardware platform implementation. Additionally, it analyzes the difficulties and challenges in the edge deployment of SNNs and points out possible solutions to these challenges.