Video restoration aims at restoring multiple high-quality frames from multiple low-quality frames. Existing video restoration methods generally fall into two extreme cases, i.e., they either restore all frames in parallel or restore the video frame by frame in a recurrent way, which would result in different merits and drawbacks. Typically, the former has the advantage of temporal information fusion. However, it suffers from large model size and intensive memory consumption; the latter has a relatively small model size as it shares parameters across frames; however, it lacks long-range dependency modeling ability and parallelizability. In this paper, we attempt to integrate the advantages of the two cases by proposing a recurrent video restoration transformer, namely RVRT. RVRT processes local neighboring frames in parallel within a globally recurrent framework which can achieve a good trade-off between model size, effectiveness, and efficiency. Specifically, RVRT divides the video into multiple clips and uses the previously inferred clip feature to estimate the subsequent clip feature. Within each clip, different frame features are jointly updated with implicit feature aggregation. Across different clips, the guided deformable attention is designed for clip-to-clip alignment, which predicts multiple relevant locations from the whole inferred clip and aggregates their features by the attention mechanism. Extensive experiments on video super-resolution, deblurring, and denoising show that the proposed RVRT achieves state-of-the-art performance on benchmark datasets with balanced model size, testing memory and runtime.