Indoor radar perception has seen rising interest due to affordable costs driven by emerging automotive imaging radar developments and the benefits of reduced privacy concerns and reliability under hazardous conditions (e.g., fire and smoke). However, existing radar perception pipelines fail to account for distinctive characteristics of the multi-view radar setting. In this paper, we propose Radar dEtection TRansformer (RETR), an extension of the popular DETR architecture, tailored for multi-view radar perception. RETR inherits the advantages of DETR, eliminating the need for hand-crafted components for object detection and segmentation in the image plane. More importantly, RETR incorporates carefully designed modifications such as 1) depth-prioritized feature similarity via a tunable positional encoding (TPE); 2) a tri-plane loss from both radar and camera coordinates; and 3) a learnable radar-to-camera transformation via reparameterization, to account for the unique multi-view radar setting. Evaluated on two indoor radar perception datasets, our approach outperforms existing state-of-the-art methods by a margin of 15.38+ AP for object detection and 11.91+ IoU for instance segmentation, respectively. Our implementation is available at https://github.com/merlresearch/radar-detection-transformer.