In this paper, we propose Local Curvelet Binary Patterns (LCBP) and Learned Local Curvelet Patterns (LLCP) for presenting the local features of facial images. The proposed methods are based on Curvelet transform which can overcome the weakness of traditional Gabor wavelets in higher dimensions, and better capture the curve singularities and hyperplane singularities of facial images. LCBP can be regarded as a combination of Curvelet features and LBP operator while LLCP designs several learned codebooks from patch sets, which are constructed by sampling patches from Curvelet filtered facial images. Each facial image can be encoded into multiple pattern maps and block-based histograms of these patterns are concatenated into an histogram sequence to be used as a face descriptor. During the face representation phase, one input patch is encoded by one pattern in LCBP while multi-patterns in LLCP. Finally, an effective classifier called Weighted Histogram Spatially constrained Earth Mover's Distance (WHSEMD) which utilizes the discriminative powers of different facial parts, the different patterns and the spatial information of face is proposed. Performance assessment in face recognition and gender estimation under different challenges shows that the proposed approaches are superior than traditional ones.