Holographic near-eye displays can deliver high-quality three-dimensional (3D) imagery with focus cues. However, the content resolution required to simultaneously support a wide field of view and a sufficiently large eyebox is enormous. The consequent data storage and streaming overheads pose a big challenge for practical virtual and augmented reality (VR/AR) applications. We present a deep-learning-based method for efficiently compressing complex-valued hologram images and videos. We demonstrate superior performance over the conventional image and video codecs.