Sequence classification has a broad range of applications such as genomic analysis, information retrieval, health informatics, finance, and abnormal detection. Different from the classification task on feature vectors, sequences do not have explicit features. Even with sophisticated feature selection techniques, the dimensionality of potential features may still be very high and the sequential nature of features is difficult to capture. This makes sequence classification a more challenging task than classification on feature vectors. In this paper, we present a brief review of the existing work on sequence classification. We summarize the sequence classification in terms of methodologies and application domains. We also provide a review on several extensions of the sequence classification problem, such as early classification on sequences and semi-supervised learning on sequences.