With the growing popularity of resource sharing and shared resources, large volumes of complex data of different types are collected automatically. Traditional data mining algorithms generally have problems and challenges including huge memory cost, low processing speed, and inadequate hard disk space. For sequential pattern mining (SPM), it is used in a wide variety of real-life applications. However, it is more complex and challenging than frequent itemset mining, and also suffers from the above challenges when handling the large-scale data. To solve these problems, mining sequential patterns in a parallel computing environment has emerged as an important issue with many applications. In this paper, an in-depth survey of the current status of parallel sequential pattern mining (PSPM) is investigated and provided, including detailed categorization of traditional serial SPM approaches, and state of the art parallel SPM. We review the related work of PSPM in detail, including partition-based algorithms for PSPM, Apriori-based PSPM, pattern growth based PSPM, and hybrid algorithms for PSPM, and provide deep description (i.e., characteristics, advantages, and disadvantages) of each parallel approach of PSPM. Some advanced topics for PSPM and the related open-source software are further reviewed in details. Finally, we summarize some challenges and opportunities of PSPM in the big data era. A Survey of Parallel Sequential Pattern Mining