This paper provides a comprehensive survey of PageRank, covering its basic model, solution methods, storage issues, convergence properties, and potential alterations. It introduces new results, references, and future research directions. The paper begins by reviewing the basic PageRank model, which uses a Markov chain to determine the importance of web pages. It discusses the challenges of storing large matrices and the use of compression techniques. The paper then delves into solution methods, including the power method and linear system formulations, and explores acceleration techniques to improve computational efficiency. It also addresses the impact of dangling nodes on PageRank and presents methods to handle them. The paper concludes with a discussion on the convergence criteria and the importance of correct ordering in the PageRank vector.This paper provides a comprehensive survey of PageRank, covering its basic model, solution methods, storage issues, convergence properties, and potential alterations. It introduces new results, references, and future research directions. The paper begins by reviewing the basic PageRank model, which uses a Markov chain to determine the importance of web pages. It discusses the challenges of storing large matrices and the use of compression techniques. The paper then delves into solution methods, including the power method and linear system formulations, and explores acceleration techniques to improve computational efficiency. It also addresses the impact of dangling nodes on PageRank and presents methods to handle them. The paper concludes with a discussion on the convergence criteria and the importance of correct ordering in the PageRank vector.