  Non-Hermitian quantum theories have been applied in many other areas of
physics. In this note, I will briefly review recent developments in the
formulation of non-Hermitian quantum field theories, highlighting features that
are unique compared to Hermitian theories. I will touch upon their crucial
discrete symmetries and how continuous symmetry properties are borne out,
including Noether's theorem, the Goldstone theorem and the Englert-Brout-Higgs
mechanism. As examples, I will describe a non-Hermitian supersymmetric theory,
and draw attention to non-Hermitian deformations of (scalar) QED, the
Higgs-Yukawa theory and flavour oscillations, with potential implications for
non-Hermitian model building in the neutrino sector. Together, these results
pave the way for a systematic programme for building non-Hermitian extensions
of the Standard Model of particle physics.
