  Non-Hermitian Hamiltonians provide an alternative perspective on the dynamics
of quantum and classical systems coupled non-conservatively to an environment.
Once primarily an interest of mathematical physicists, the theory of
non-Hermitian Hamiltonians has solidified and expanded to describe various
physically observable phenomena in optical, photonic, and condensed matter
systems. Self-consistent descriptions of quantum mechanics based on
non-Hermitian Hamiltonians have been developed and continue to be refined. In
particular, non-Hermitian frameworks to describe magnonic and hybrid magnonic
systems have gained popularity and utility in recent years, with new insights
into the magnon topology, transport properties, and phase transitions coming
into view. Magnonic systems are in many ways a natural platform in which to
realize non-Hermitian physics because they are always coupled to a surrounding
environment and exhibit lossy dynamics. In this perspective we review recent
progress in non-Hermitian frameworks to describe magnonic and hybrid magnonic
systems, such as cavity magnonic systems and magnon-qubit coupling schemes. We
discuss progress in understanding the dynamics of inherently lossy magnetic
systems as well as systems with gain induced by externally applied spin
currents. We enumerate phenomena observed in both purely magnonic and hybrid
magnonic systems which can be understood through the lens of non-Hermitian
physics, such as PT and Anti-PT-symmetry breaking, dynamical magnetic phase
transitions, non-Hermitian skin effect, and the realization of exceptional
points and surfaces. Finally, we comment on some open problems in the field and
discuss areas for further exploration.
