We present Recurrent Vision Transformers (RVTs), a novel backbone for object detection with event cameras. Event cameras provide visual information with sub-millisecond latency at a high-dynamic range and with strong robustness against motion blur. These unique properties offer great potential for low-latency object detection and tracking in time-critical scenarios. Prior work in event-based vision has achieved outstanding detection performance but at the cost of substantial inference time, typically beyond 40 milliseconds. By revisiting the high-level design of recurrent vision backbones, we reduce inference time by a factor of 6 while retaining similar performance. To achieve this, we explore a multi-stage design that utilizes three key concepts in each stage: First, a convolutional prior that can be regarded as a conditional positional embedding. Second, local and dilated global self-attention for spatial feature interaction. Third, recurrent temporal feature aggregation to minimize latency while retaining temporal information. RVTs can be trained from scratch to reach state-of-the-art performance on event-based object detection - achieving an mAP of 47.2% on the Gen1 automotive dataset. At the same time, RVTs offer fast inference (<12 ms on a T4 GPU) and favorable parameter efficiency (5 times fewer than prior art). Our study brings new insights into effective design choices that can be fruitful for research beyond event-based vision.