Continual learning (CL) promises to allow neural networks to learn from continuous streams of inputs, instead of IID (independent and identically distributed) sampling, which requires random access to a full dataset. This would allow for much smaller storage requirements and self-sufficiency of deployed systems that cope with natural distribution shifts, similarly to biological learning. We focus on video CL employing a rehearsal-based approach, which reinforces past samples from a memory buffer. We posit that part of the reason why practical video CL is challenging is the high memory requirements of video, further exacerbated by long-videos and continual streams, which are at odds with the common rehearsal-buffer size constraints. To address this, we propose to use compressed vision, i.e. store video codes (embeddings) instead of raw inputs, and train a video classifier by IID sampling from this rolling buffer. Training a video compressor online (so not depending on any pre-trained networks) means that it is also subject to catastrophic forgetting. We propose a scheme to deal with this forgetting by refreshing video codes, which requires careful decompression with a previous version of the network and recompression with a new one. We name our method Continually Refreshed Amodal Memory (CRAM). We expand current video CL benchmarks to large-scale settings, namely EpicKitchens-100 and Kinetics-700, storing thousands of relatively long videos in under 2 GB, and demonstrate empirically that our video CL method outperforms prior art with a significantly reduced memory footprint.