Summary: Recently, distance metric learning has become one of the most attractive research areas in computer vision and pattern recognition. How to learn an effective distance metric to measure the similarity between subjects is a key problem. A large number of algorithms have been proposed to deal with supervised distance metric learning. This paper reviews and discusses recently developed algorithms for supervised distance metric learning. Based on the partition of pairwise constraints and non-pairwise constraints, some representative algorithms are introduced and their respective pros and cons are analyzed. The prospects for future development and suggestions for further research work are presented in the end.