Similarity measure is an important concept in time series data mining. For many data mining algorithms, whether it can be used in combination with a suitable time series similarity measure method has a key influence on mining performance. However, there is no uniform definition and measure of similarity. Therefore, we first introduce the most popular similarity measures, and analyze the advantages and disadvantages of each measure. Then, the new interpretations of the time series similarity and the corresponding measures are discussed. Furthermore, we analyze the applications of similarity measures in clustering, classification and regression of time series data, and the relationship between similarity measure and mining precision. Finally, several directions for the future research are given.