Sequential pattern mining is an important data mining problem with broad applications. However,it is also a challenging problem since the mining may have to generate or examine a combinatorially explosive number of intermediate subsequences. Recent studies have developed two major classes of sequential pattern mining methods: (1) a candidate generation-and-test approach, represented by (i) GSP, a horizontal format-based sequential pattern mining method, and (ii) SPADE, a vertical format-based method; and (2) a pattern-growth method, represented by PrefixSpan and its further extensions, such as gSpan for mining structured patterns. In this study, we perform a systematic introduction and presentation of the pattern-growth methodology and study its principles and extensions. We first introduce two interesting pattern-growth algorithms, FreeSpan and PrefixSpan, for efficient sequential pattern mining. Then we introduce gSpan for mining structured patterns using the same methodology. Their relative performance in large databases is presented and analyzed. Several extensions of these methods are also discussed in the paper, including mining multi-level, multi-dimensional patterns and mining constraint-based patterns.