Recent interest in systems with excitations that have sub-dimensional mobility and conserved higher-multipole moments has motivated an investigation of models with so-called subsystem symmetry, in which conservation laws apply not to the system as a whole, but rather to sub manifolds within the system, such as families of lattice planes. I will discuss analogs of symmetry protection in these phases, and its relation to anomalies in the corresponding field theoretical description, which involves tensor gauge fields.