Quantum walks are quantum mechanical counterparts of classical random walks and have been shown to be a universal model of quantum computation. This paper reviews theoretical advances on discrete and continuous-time quantum walks, the role of randomness in quantum walks, connections between mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, and experimental proposals for discrete-time quantum walks. It also summarizes algorithms based on both discrete and continuous-time quantum walks and highlights the computational universality of both types of quantum walks. Quantum walks are important in quantum computation as they provide a powerful tool for building quantum algorithms. They have been shown to be universal, meaning they can simulate any quantum computation. The paper discusses the differences between discrete and continuous quantum walks, with discrete walks applying evolution operators in discrete time steps and continuous walks applying them at any time. The paper also explores the properties of quantum walks on graphs, including limit theorems, localization, and the effects of decoherence. The paper reviews several quantum algorithms based on quantum walks, including those for searching in an unordered list, the element distinctness problem, and the triangle problem. It also discusses the role of randomness in quantum walks and the connections between mathematical models of coined discrete quantum walks and continuous quantum walks. The paper concludes with a discussion of the computational universality of both continuous and discrete-time quantum walks, highlighting their importance in quantum computation.Quantum walks are quantum mechanical counterparts of classical random walks and have been shown to be a universal model of quantum computation. This paper reviews theoretical advances on discrete and continuous-time quantum walks, the role of randomness in quantum walks, connections between mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, and experimental proposals for discrete-time quantum walks. It also summarizes algorithms based on both discrete and continuous-time quantum walks and highlights the computational universality of both types of quantum walks. Quantum walks are important in quantum computation as they provide a powerful tool for building quantum algorithms. They have been shown to be universal, meaning they can simulate any quantum computation. The paper discusses the differences between discrete and continuous quantum walks, with discrete walks applying evolution operators in discrete time steps and continuous walks applying them at any time. The paper also explores the properties of quantum walks on graphs, including limit theorems, localization, and the effects of decoherence. The paper reviews several quantum algorithms based on quantum walks, including those for searching in an unordered list, the element distinctness problem, and the triangle problem. It also discusses the role of randomness in quantum walks and the connections between mathematical models of coined discrete quantum walks and continuous quantum walks. The paper concludes with a discussion of the computational universality of both continuous and discrete-time quantum walks, highlighting their importance in quantum computation.