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In this paper, we study the problem of robust feature extraction based on l2, 1 regularized correntropy in both theoretical and algorithmic manner. In theoretical part, we point out that an l2, 1-norm minimization can be justified from the viewpoint of half-quadratic (HQ) optimization, which facilitates convergence study and algorithmic development. In particular, a general formulation is accordingly proposed to unify l1-norm and l2, 1-norm minimization within a common framework. In algorithmic part, we propose an l2, 1 regularized correntropy algorithm to extract informative features meanwhile to remove outliers from training data. A new alternate minimization algorithm is also developed to optimize the non-convex correntropy objective. In terms of face recognition, we apply the proposed method to obtain an appearance-based model, called Sparse-Fisherfaces. Extensive experiments show that our method can select robust and sparse features, and outperforms several state-of-the-art subspace methods on large-scale and open face recognition datasets.