We introduce an approach for recovering the 6D pose of multiple known objects in a scene captured by a set of input images with unknown camera viewpoints. First, we present a single-view single-object 6D pose estimation method, which we use to generate 6D object pose hypotheses. Second, we develop a robust method for matching individual 6D object pose hypotheses across different input images in order to jointly estimate camera viewpoints and 6D poses of all objects in a single consistent scene. Our approach explicitly handles object symmetries, does not require depth measurements, is robust to missing or incorrect object hypotheses, and automatically recovers the number of objects in the scene. Third, we develop a method for global scene refinement given multiple object hypotheses and their correspondences across views. This is achieved by solving an object-level bundle adjustment problem that refines the poses of cameras and objects to minimize the reprojection error in all views. We demonstrate that the proposed method, dubbed CosyPose, outperforms current state-of-the-art results for single-view and multi-view 6D object pose estimation by a large margin on two challenging benchmarks: the YCB-Video and T-LESS datasets. Code and pre-trained models are available on the project webpage https://www.di.ens.fr/willow/research/cosypose/.