Optical flow is a classical task that is important to the vision community. Classical optical flow estimation uses two frames as input, whilst some recent methods consider multiple frames to explicitly model long-range information. The former ones limit their ability to fully leverage temporal coherence along the video sequence; and the latter ones incur heavy computational overhead, typically not possible for real-time flow estimation. Some multi-frame-based approaches even necessitate unseen future frames for current estimation, compromising real-time applicability in safety-critical scenarios. To this end, we present MemFlow, a real-time method for optical flow estimation and prediction with memory. Our method enables memory read-out and update modules for aggregating historical motion information in real-time. Furthermore, we integrate resolution-adaptive re-scaling to accommodate diverse video resolutions. Besides, our approach seamlessly extends to the future prediction of optical flow based on past observations. Leveraging effective historical motion aggregation, our method outperforms VideoFlow with fewer parameters and faster inference speed on Sintel and KITTI-15 datasets in terms of generalization performance. At the time of submission, MemFlow also leads in performance on the 1080p Spring dataset. Codes and models will be available at: https://dqiaole.github.io/MemFlow/.