We present an implicit video representation for occlusions, appearance, and motion disentanglement from monocular videos, which we call Video SPatiotemporal Splines (VideoSPatS). Unlike previous methods that map time and coordinates to deformation and canonical colors, our VideoSPatS maps input coordinates into Spatial and Color Spline deformation fields ${\mathcal{D}_{\text{s}}}$ and ${\mathcal{D}_c}$, which disentangle motion and appearance in videos. With spline-based parametrization, our method naturally generates temporally consistent flow and guarantees long-term temporal consistency, which is crucial for convincing video editing. Using multiple prediction branches, our VideoSPatS model also performs layer separation between the latent video and the selected occluder. By disentangling occlusions, appearance, and motion, our method enables better spatiotemporal modeling and editing of diverse videos, including in-the-wild talking head videos with challenging occlusions, shadows, and specularities while maintaining an appropriate canonical space for editing. We also present general video modeling results on the DAVIS and CoDeF datasets, as well as our own talking head video dataset collected from open-source web videos. Extensive ablations show the combination of ${\mathcal{D}_{\text{s}}}$ and ${\mathcal{D}_c}$ under neural splines can overcome motion and appearance ambiguities, paving the way for more advanced video editing models. Visit our project site1.