Sequential Pattern Mining （SPM） aims to discover interesting patterns or rules from databases to support and guide user decision-making. In recent years， research on algorithms related to SPM goes deeper and deeper increasingly. With the emergence of large-scale data， many sequential algorithms suitable for parallel environments have been proposed. Therefore， a review of the existing sequential and parallel sequential mining algorithms was presented. Firstly， for sequential pattern serial mining algorithms， structured classification was performed， which means that the algorithms were categorized on the basis of adopted data structures they use， such as tree structure， list structure， and link structure， the advantages and disadvantages of different structures were summarized comprehensively and the strengths and weaknesses of each algorithm were summed up in detail. Secondly， for sequential pattern parallel mining algorithms， for the first time， the existing distributed frameworks were classified according to different characteristics of storage structures， the advantages and disadvantages of different distributed frameworks were analyzed and the parallel algorithms were introduced and analyzed on the basis of these frameworks. Finally， future research directions were discussed to address the shortcomings of the existing SPM algorithms.