  The article reviews the theory of open quantum system from a perspective of
the non-Hermiticity that emerges from the environment with an infinite number
of degrees of freedom. The non-Hermiticity produces resonant states with
complex eigenvalues, resulting in peak structures in scattering amplitudes and
transport coefficients. After introducing the definition of resonant states
with complex eigenvalues, we answer typical questions regarding the
non-Hermiticity of open quantum systems. What is the physical meaning of the
complex eigenmomenta and eigenenergies? How and why do the resonant states
break the time-reversal symmetry that the system observes? Can we make the
probabilistic interpretation of the resonant states with diverging wave
functions? What is the physical meaning of the divergence of the wave
functions? We also present an alternative way of finding resonant states,
namely the Feshbach formalism, in which we eliminate the infinite number of the
environmental degrees of freedom. In this formalism, we attribute the
non-Hermiticity to the introduction of the retarded and advanced Green's
functions.
