Parametric 3D models have enabled a wide variety of tasks in computer graphics and vision, such as modeling human bodies, faces, and hands. However, the construction of these parametric models is often tedious, as it requires heavy manual tweaking, and they struggle to represent additional complexity and details such as wrinkles or clothing. To this end, we propose Neural Parametric Models (NPMs), a novel, learned alternative to traditional, parametric 3D models, which does not require hand-crafted, object-specific constraints. In particular, we learn to disentangle 4D dynamics into latent-space representations of shape and pose, leveraging the flexibility of recent developments in learned implicit functions. Crucially, once learned, our neural parametric models of shape and pose enable optimization over the learned spaces to fit to new observations, similar to the fitting of a traditional parametric model, e.g., SMPL. This enables NPMs to achieve a significantly more accurate and detailed representation of observed deformable sequences. We show that NPMs improve notably over both parametric and non-parametric state of the art in reconstruction and tracking of monocular depth sequences of clothed humans and hands. Latent-space interpolation as well as shape / pose transfer experiments further demonstrate the usefulness of NPMs.