This talk will discuss 3D data priors and their important connection to 3D representations. Choosing the right representation, we can have abstract control over which information is learned from data and how we can use it during inference, which leads to more effective solutions than simply learning everything end-to-end. Thus, the focus of my research and this talk will be on representations with important properties, such as data efficiency and useful equi- and invariances, which enable the formulation of sophisticated, task-specific data priors. These presented concepts are showcased on examples from my and collaborating groups, e.g., as data priors for reconstructing objects or object interaction sequences from incomplete observations.