We address efficient and structure-aware 3D scene representation from images. Nerflets are our key contribution-- a set of local neural radiance fields that together represent a scene. Each nerflet maintains its own spatial position, orientation, and extent, within which it contributes to panoptic, density, and radiance reconstructions. By leveraging only photometric and inferred panoptic image supervision, we can directly and jointly optimize the parameters of a set of nerflets so as to form a decomposed representation of the scene, where each object instance is represented by a group of nerflets. During experiments with indoor and outdoor environments, we find that nerflets: (1) fit and approximate the scene more efficiently than traditional global NeRFs, (2) allow the extraction of panoptic and photometric renderings from arbitrary views, and (3) enable tasks rare for NeRFs, such as 3D panoptic segmentation and interactive editing.