Unsupervised learning of 3D-aware generative adversarial networks (GANs) using only collections of single-view 2D photographs has very recently made much progress. These 3D GANs, however, have not been demonstrated for human bodies and the generated radiance fields of existing frameworks are not directly editable, limiting their applicability in downstream tasks. We propose a solution to these challenges by developing a 3D GAN framework that learns to generate radiance fields of human bodies or faces in a canonical pose and warp them using an explicit deformation field into a desired body pose or facial expression. Using our framework, we demonstrate the first high-quality radiance field generation results for human bodies. Moreover, we show that our deformation-aware training procedure significantly improves the quality of generated bodies or faces when editing their poses or facial expressions compared to a 3D GAN that is not trained with explicit deformations.