Feature selection is an important data pre-processing step in pattern recognition and data mining. It is effective in reducing dimensionality and redundancy among the selected features, and increasing the performance of learning algorithm and generating information-rich features subset. In this regard, the chapter reports on a rough set-based feature selection algorithm called maximum relevance-maximum significance (MRMS), and its applications on quantitative structure activity relationship (QSAR) and gene expression data. It selects a set of features from a high-dimensional data set by maximizing the relevance and significance of the selected features. A theoretical analysis is reported to justify the use of both relevance and significance criteria for selecting a reduced feature set with high predictive accuracy. The importance of rough set theory for computing both relevance and significance of the features is also established. The performance of the MRMS algorithm, along with a comparison with other related methods, is studied on three QSAR data sets using the R 2 statistic of support vector regression method, and on five cancer and two arthritis microarray data sets by using the predictive accuracy of the K-nearest neighbor rule and support vector machine. © Springer-Verlag Berlin Heidelberg 2013.