We introduce a novel matching algorithm, called DeepMatching, to compute dense correspondences between images. DeepMatching relies on a hierarchical, multi-layer, correlational architecture designed for matching images and was inspired by deep convolutional approaches. The proposed matching algorithm can handle non-rigid deformations and repetitive textures and efficiently determines dense correspondences in the presence of significant changes between images. We evaluate the performance of DeepMatching, in comparison with state-of-the-art matching algorithms, on the Mikolajczyk (Mikolajczyk et al. A comparison of affine region detectors, 2005), the MPI-Sintel (Butler et al. A naturalistic open source movie for optical flow evaluation, 2012) and the Kitti (Geiger et al. Vision meets robotics: The KITTI dataset, 2013) datasets. DeepMatching outperforms the state-of-the-art algorithms and shows excellent results in particular for repetitive textures. We also apply DeepMatching to the computation of optical flow, called DeepFlow, by integrating it in the large displacement optical flow (LDOF) approach of Brox and Malik (Large displacement optical flow: descriptor matching in variational motion estimation, 2011). Additional robustness to large displacements and complex motion is obtained thanks to our matching approach. DeepFlow obtains competitive performance on public benchmarks for optical flow estimation.