This paper surveys efficient algorithms for computing Personalized PageRank (PPR), a measure of node proximity in large graphs. PPR extends Google's PageRank by allowing personalized queries and has been widely applied in network analysis, graph mining, and machine learning. Despite extensive research, efficient PPR computation remains challenging, and there is a lack of systematic comparisons of existing algorithms. This paper reviews various PPR algorithms, classifying them based on the types of queries they address and reviewing their methodologies and contributions. It also discusses representative algorithms for computing PPR on dynamic graphs and in parallel or distributed environments. PPR is defined as the probability that an α-discounted random walk from a source node s terminates at a target node t. It can be computed using algebraic methods, random walks, or approximation techniques. The paper introduces five basic techniques for PPR computation: the Monte Carlo method, Power Iteration, Forward Push, Reverse Power Iteration, and Backward Push. These techniques are analyzed in terms of their efficiency, error bounds, and applicability to different query types. The paper also discusses the computational complexity of PPR algorithms, noting that methods based on random walks or algebraic techniques can achieve sublinear time complexity for certain queries. However, exact computation of PPR for large graphs is computationally expensive, and approximation techniques are often necessary for efficiency. The paper highlights the importance of error measures, such as absolute and relative error, in evaluating the accuracy of PPR computations. In addition to the basic techniques, the paper reviews recent PPR algorithms that have been developed for specific applications, such as local graph clustering, node embedding, and graph neural networks. These algorithms leverage PPR for tasks like clustering, embedding, and neural network design, demonstrating the versatility of PPR in graph analysis. The paper also discusses the challenges of computing PPR on dynamic graphs and in distributed environments, and highlights the need for efficient algorithms that can handle large-scale graph data. Overall, the paper provides a comprehensive overview of PPR computation, emphasizing the importance of efficient algorithms for large graphs and the need for further research in this area. It serves as a reference for researchers and practitioners interested in the efficient computation of PPR in various applications.This paper surveys efficient algorithms for computing Personalized PageRank (PPR), a measure of node proximity in large graphs. PPR extends Google's PageRank by allowing personalized queries and has been widely applied in network analysis, graph mining, and machine learning. Despite extensive research, efficient PPR computation remains challenging, and there is a lack of systematic comparisons of existing algorithms. This paper reviews various PPR algorithms, classifying them based on the types of queries they address and reviewing their methodologies and contributions. It also discusses representative algorithms for computing PPR on dynamic graphs and in parallel or distributed environments. PPR is defined as the probability that an α-discounted random walk from a source node s terminates at a target node t. It can be computed using algebraic methods, random walks, or approximation techniques. The paper introduces five basic techniques for PPR computation: the Monte Carlo method, Power Iteration, Forward Push, Reverse Power Iteration, and Backward Push. These techniques are analyzed in terms of their efficiency, error bounds, and applicability to different query types. The paper also discusses the computational complexity of PPR algorithms, noting that methods based on random walks or algebraic techniques can achieve sublinear time complexity for certain queries. However, exact computation of PPR for large graphs is computationally expensive, and approximation techniques are often necessary for efficiency. The paper highlights the importance of error measures, such as absolute and relative error, in evaluating the accuracy of PPR computations. In addition to the basic techniques, the paper reviews recent PPR algorithms that have been developed for specific applications, such as local graph clustering, node embedding, and graph neural networks. These algorithms leverage PPR for tasks like clustering, embedding, and neural network design, demonstrating the versatility of PPR in graph analysis. The paper also discusses the challenges of computing PPR on dynamic graphs and in distributed environments, and highlights the need for efficient algorithms that can handle large-scale graph data. Overall, the paper provides a comprehensive overview of PPR computation, emphasizing the importance of efficient algorithms for large graphs and the need for further research in this area. It serves as a reference for researchers and practitioners interested in the efficient computation of PPR in various applications.