We propose a new matching algorithm, called DeepMatching, to compute dense correspondences between images. DeepMatching relies on a deep, multi-layer, convolutional architecture designed for matching images. The proposed matching algorithm can handle non-rigid deformations and repetitive textures, and can therefore efficiently determine 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 resp. the Mikolajczyk, the MPI-Sintel and the Kitti datasets. The performance measure is "Accuracy@T" , that is the percentage of correct pixels for a specified error threshold of T pixels. Deep-Matching outperforms the state-of-the-art algorithms in terms of accuracy@T and shows excellent results in particular for repetitive textures. We also propose a method for estimating optical flow, called DeepFlow, by integrating a DeepMatching term in a variational energy minimization approach. Robustness to large displacements is obtained due to this matching term. DeepFlow obtains competitive performance on public benchmarks for optical flow estimation. In particular, DeepFlow obtains state-of-the-art results on the MPI-Sintel dataset.