Temporal data mining (TDM) has been attracting more and more interest from a vast range of domains, from engineering to finance. Similarity discovery technique concentrates on the evolution and development of data, attempting to discover the similarity regularity of dynamic data evolution. The most significant techniques developed in recent researches to deal with similarity discovery in TDM are analyzed. Firstly, the definitions of three categories of temporal data, time series, event sequence, and transaction sequence are presented, and then the current techniques and methods related to various sequences with similarity measures, representations, searching, and various mining tasks getting involved are classified and discussed. Finally, some future research trends on this area are discussed.