Anomalous symmetries are fundamental to modern physics, often characterized by their appearance on the boundaries of symmetry-protected topological phases and by obstructions to gauging or onsite realization. It is commonly believed that these features are equivalent signatures of anomaly. In this talk, I will present a new class of anomaly-free symmetries that challenge this conventional wisdom: these symmetries cannot be realized onsite nor gauged, yet still admit a unique, gapped, symmetric ground state. I will then outline the classification of obstructions to onsiteness and explain their connection to a new family of symmetric quantum cellular automata in three dimensions.