With the development of bioinformatics, gene expression microarray and image recognition, classification on high-dimensional and small-sample-size data has become a challenging task in data ming, machine learning and pattern recognition as well. High-dimensional and small-sample-size data may cause the problem of "curse of dimensionality" and overfitting. Feature selection can prevent the "curse of dimensionality" effectively and promote the generalization ability of classification mode, and thus become a hot research topic. Accordingly, some recent development of world-wide research on feature selection in high-dimensional and small-sample-size classification was briefly reviewed. Firstly, the nature of high-dimensional and small-sample feature selection was analyzed. Secondly, according to their essential difference, feature selection algorithms for high-dimensional and small-sample-size classification were divided into four categories and compared to summarize their advantages and disadvantages. Finally, challenges and prospects for future trends of feature selection in high-dimensional small-sample-size data were proposed.