We present Non-Rigid Neural Radiance Fields (NR-NeRF), a reconstruction and novel view synthesis approach for general non-rigid dynamic scenes. Our approach takes RGB images of a dynamic scene as input (e.g., from a monocular video recording), and creates a high-quality space-time geometry and appearance representation. We show that a single handheld consumer-grade camera is sufficient to synthesize sophisticated renderings of a dynamic scene from novel virtual camera views, e.g. a `bullet-time' video effect. NR-NeRF disentangles the dynamic scene into a canonical volume and its deformation. Scene deformation is implemented as ray bending, where straight rays are deformed non-rigidly. We also propose a novel rigidity network to better constrain rigid regions of the scene, leading to more stable results. The ray bending and rigidity network are trained without explicit supervision. Our formulation enables dense correspondence estimation across views and time, and compelling video editing applications such as motion exaggeration. Our code is available.