In the recent years with the advancement in technology, a lot of information is available in different formats and extracting the knowledge from that data has become a very difficult task. Due to the vast amount of information available on the web, users are finding it difficult to extract relevant information or create new knowledge using information available on the web. To solve this problem Web mining techniques are used to discover the interesting patterns from the hidden data. Web Usage Mining (WUM), which is one of the subset of Web Mining helps in extracting the hidden knowledge present in the Web log files, in recognizing various interests of web users and also in discovering customer behaviours. Web Usage mining includes different phases of data mining techniques called Data Pre-processing, Pattern Discovery & Pattern Analysis. This paper presents an updated focused survey on various sequential pattern mining algorithms like apriori-based algorithm, Breadth First Search-based strategy, Depth First Search strategy, sequential closed-pattern algorithm and Incremental pattern mining algorithm which are used in Pattern Discovery Phase of WUM. At last, a comparison is done based on the important key features present in these algorithms. This study gives us better understanding of the approaches of sequential pattern mining.