Video compression allows for efficient storage and transmission of data, benefiting imaging and vision applications, e.g. computational imaging, photography, and displays by delivering high-quality videos. To exploit more informative contexts of video, we propose DVCL, a novel Deep Video Compression based on Long-range Temporal Context Learning. Aiming at high coding performance, this new compression paradigm makes full use of long-range temporal correlations derived from multiple reference frames to learn richer contexts. Firstly, motion vectors (MVs) are estimated to represent the motion relations of video by MV module. By employing MVs, a long-range temporal context learning (LTCL) module is presented to extract context information from multiple reference frames, such that a more accurate and informative temporal contexts can be learned and constructed. The long-range temporal contexts serve as conditions by feeding into contextual module, which generates the predicted frames by contextual encoder and decoder. Moreover, to address the challenge of imbalanced training, we develop a multi-stage training strategy to ensure the whole DVCL framework is trained progressively and stably. Extensive experiments demonstrate the proposed DVCL achieves the highest objective and subjective quality, while maintaining relatively low complexity. Specifically, 25.30% and 45.75% bitrate savings on average can be obtained than x265 codec at the same PSNR and MS-SSIM, respectively. Validation experiments also show that DVCL can benefit computational photography applications, e.g., super-resolution and frame interpolation.