This review provides a comprehensive overview of quantum walk computing, including its theory, implementation, and applications. Quantum walks, as the quantum counterpart of classical random walks, have been extensively studied for their potential to achieve beyond classical computing power. They have been applied in various fields such as quantum algorithms, quantum simulation, quantum information processing, and graph-theoretic applications. The review highlights the advantages of quantum walks, such as faster evolution and unique probability distributions, and discusses their challenges and future prospects. The paper begins by introducing the classical and quantum walk models, including discrete-time and continuous-time quantum walks, and comparing their characteristics. It then delves into the physical implementations of quantum walks, covering both analogue and digital approaches, and discusses the progress in experimental demonstrations. The review also explores the applications of quantum walks, such as quantum computing, quantum simulation, and graph-theoretic problems, and addresses the computational advantages of quantum walks over classical algorithms. Finally, the paper discusses the challenges facing quantum walk computing, particularly in the noisy intermediate-scale quantum (NISQ) era, and outlines the potential for practical quantum computers in the near future. The review concludes with an outlook on the future of quantum walk computing, emphasizing the need for further research and development to overcome current limitations.This review provides a comprehensive overview of quantum walk computing, including its theory, implementation, and applications. Quantum walks, as the quantum counterpart of classical random walks, have been extensively studied for their potential to achieve beyond classical computing power. They have been applied in various fields such as quantum algorithms, quantum simulation, quantum information processing, and graph-theoretic applications. The review highlights the advantages of quantum walks, such as faster evolution and unique probability distributions, and discusses their challenges and future prospects. The paper begins by introducing the classical and quantum walk models, including discrete-time and continuous-time quantum walks, and comparing their characteristics. It then delves into the physical implementations of quantum walks, covering both analogue and digital approaches, and discusses the progress in experimental demonstrations. The review also explores the applications of quantum walks, such as quantum computing, quantum simulation, and graph-theoretic problems, and addresses the computational advantages of quantum walks over classical algorithms. Finally, the paper discusses the challenges facing quantum walk computing, particularly in the noisy intermediate-scale quantum (NISQ) era, and outlines the potential for practical quantum computers in the near future. The review concludes with an outlook on the future of quantum walk computing, emphasizing the need for further research and development to overcome current limitations.