While today's video recognition systems parse snapshots or short clips accurately, they cannot connect the dots and reason across a longer range of time yet. Most existing video architectures can only process <5 seconds of a video without hitting the computation or memory bottlenecks. In this paper, we propose a new strategy to overcome this challenge. Instead of trying to process more frames at once like most existing methods, we propose to process videos in an online fashion and cache memory at each iteration. Through the memory, the model can reference prior context for long-term modeling, with only a marginal cost. Based on this idea, we build MeMViT, a Memory-augmented Multiscale Vision Transformer, that has a temporal support 30x longer than existing models with only 4.5% more compute; traditional methods need 3,000% more compute to do the same. On a wide range of settings, the increased temporal support enabled by MeMViT brings large gains in recognition accuracy consistently. MeMViT obtains state-of-the-art results on the AVA, EPIC-Kitchens-100 action classification, and action anticipation datasets. Code and models will be made publicly available.