We consider the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories. We begin by revisiting the derivation of Noether’s theorem and find that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant. After describing the implications of this conclusion for gauge invariance, we consider the spontaneous breakdown of global and local symmetries, and illustrate how the Goldstone theorem and the Englert-Brout-Higgs mechanism are borne out. We conclude by commenting on the potential avenues for model building in fundamental physics from the non-Hermitian deformation of the Standard Model of particle physics.