In recent years, as an important component of data mining, the classification task of MTS has received increasing attention from experts in various fields. Although there have been some research results on MTS classification methods, most of the studies in the literature focus on accuracy as the main research goal, and few of them focus on the interpretability of the results. In this paper, we summarize dozens of MTS classification algorithms with both accuracy and interpretability in three directions, introduce the principles and procedures of these methods, and analyze their advantages and disadvantages. It also provides an outlook on future research directions.