By exploiting the low-dimensional structure of high-dimensional data, sparse representation based classifiers (SRC) has recently attracted massive attention in pattern recognition. In this paper, we study a natural generalization of SRC, i.e., block sparse representation based classifiers (BSRC), which takes into account the block structure of the dictionary. Our contributions are two-fold: (1) we provide theoretical guarantees for BSRC and theoretically show that BSRC performs perfect classification for any test sample under both cases of independent subspaces and arbitrary subspaces settings; (2) we extend BSRC and propose three robust BSRC methods based on M-estimators originating in robust statistics. This is motivated by the observation that many previous representation based classifiers utilize the mean square error (MSE) criterion as the loss function, which is sensitive to outliers and complicated noises in reality. In contrast, M-estimators has shown much stronger robustness than MSE against gross corruptions. We demonstrate the efficacy of the proposed methods through experiments on both synthetic and real-world databases for block sparse recovery, handwritten digit recognition and robust face recognition.