This paper provides a comprehensive review of quantum walks, which are the quantum mechanical counterparts of classical random walks. Quantum walks have emerged as a powerful tool for building quantum algorithms and have been shown to constitute a universal model of quantum computation. The review covers both discrete and continuous-time quantum walks, exploring their theoretical foundations, the role of randomness, connections between different models, and their quantumness. It also discusses experimental proposals and realizations of discrete-time quantum walks, as well as algorithms based on these walks. A significant contribution of the paper is the demonstration of the computational universality of both continuous- and discrete-time quantum walks. The review is structured into several sections, including an introduction to classical random walks, the fundamentals of quantum walks, algorithms based on quantum walks, and the universality of quantum walks. The paper highlights the importance of quantum walks in quantum computing and their potential applications in various scientific and technological fields.This paper provides a comprehensive review of quantum walks, which are the quantum mechanical counterparts of classical random walks. Quantum walks have emerged as a powerful tool for building quantum algorithms and have been shown to constitute a universal model of quantum computation. The review covers both discrete and continuous-time quantum walks, exploring their theoretical foundations, the role of randomness, connections between different models, and their quantumness. It also discusses experimental proposals and realizations of discrete-time quantum walks, as well as algorithms based on these walks. A significant contribution of the paper is the demonstration of the computational universality of both continuous- and discrete-time quantum walks. The review is structured into several sections, including an introduction to classical random walks, the fundamentals of quantum walks, algorithms based on quantum walks, and the universality of quantum walks. The paper highlights the importance of quantum walks in quantum computing and their potential applications in various scientific and technological fields.