  We review some recent work on the occurrence of coalescing eigenstates at
exceptional points in non-Hermitian systems and their influence on physical
quantities. We particularly focus on quantum dynamics near exceptional points
in open quantum systems, which are described by an outwardly Hermitian
Hamiltonian that gives rise to a non-Hermitian effective description after one
projects out the environmental component of the system. We classify the
exceptional points into two categories: those at which two or more resonance
states coalesce and those at which at least one resonance and the partnering
anti-resonance coalesce (possibly including virtual states as well), and we
introduce several simple models to explore the dynamics for both of these
types. In the latter case of coalescing resonance and anti-resonance states, we
show that the presence of the continuum threshold plays a strong role in
shaping the dynamics, in addition to the exceptional point itself. We also
briefly discuss the special case in which the exceptional point appears
directly at the threshold.
