Nowadays we are in the big data era. The high-dimensionality ofdata imposes big challenge on how to process them effectively andefficiently. Fortunately, in practice data are not unstructured.Their samples usually lie around low-dimensional manifolds andhave high correlation among them. Such characteristics can beeffectively depicted by low rankness. As an extension to thesparsity of first order data, such as voices, low rankness is alsoan effective measure for the sparsity of second order data, suchas images. In this paper, I review the representative theories,algorithms and applications of the low rank subspace recoverymodels in data processing.