We present ONeRF, a method that automatically segments and reconstructs object instances in 3D from multi-view RGB images without any additional manual annotations. The segmented 3D objects are represented using separate Neural Radiance Fields (NeRFs) which allow for various 3D scene editing and novel view rendering. At the core of our method is an unsupervised approach using the iterative Expectation-Maximization algorithm, which effectively aggregates 2D visual features and the corresponding 3D cues from multi-views for joint 3D object segmentation and reconstruction. Unlike existing approaches that can only handle simple objects, our method produces segmented full 3D NeRFs of individual objects with complex shapes, topologies and appearance. The segmented ONeRfs enable a range of 3D scene editing, such as object transformation, insertion and deletion.