Symmetries are fundamental for the description of physical systems providing the basis for conservation laws and determining the form of the interaction between elementary particles. Less transparent is the role of symmetries in complex systems where frequently occurs the situation that different symmetries occur in different restricted spatial domains. The question is if in such a case it is possible to develop theoretical tools, capable to describe the pathway from globally valid to spatially restricted symmetries. Considering the physics of linear waves in aperiodic one-dimensional waveguides, we will show the existence of non-local, divergent free, currents which lead to local conservation laws in the presence of symmetries valid in finite space domains. These non-local currents allow the extension of Bloch and parity theorems to aperiodic, locally symmetric, systems. Furthermore, they can be used to classify perfect transmission resonances and describe the symmetry breaking in scattering in PT-symmetric waveguides.