  We review the effects of excited-state quantum phase transitions (ESQPTs) in
interacting many-body systems with finite numbers of collective degrees of
freedom. We classify typical ESQPT signatures in the spectra of energy
eigenstates with respect to the underlying classical dynamics and outline a
variety of quantum systems in which they occur. We describe thermodynamic and
dynamic consequences of ESQPTs, like those in microcanonical thermodynamics,
quantum quench dynamics, and in the response to nearly adiabatic or periodic
driving. We hint at some generalizations of the ESQPT concept in periodic
lattices and in resonant tunneling systems.
