In a number of applications, such as the analysis of gene expression data, classical questions from statistical modeling of which variables are of relevance and how these variables interact arise. This has motivated much study on variable and feature selection and a variety of statistical procedures and algorithms were proposed. In this talk, I will present a new approach for variable and feature selection which is based on learning gradients. The basic idea of this approach lies on the fact that gradients reflect the sensitivity of functions along coordinates and hence the estimation and analysis of gradients provide us the information of explanatory variables and features. The contents will include an algorithm for learning the gradient and its implementation, a variable and feature selection criterion, the utility on some interesting datasets, and its interpretation in manifold setting.