Electronically excited states of
molecules are at the heart of
photochemistry, photophysics, as well as photobiology and also play
a role in material science. Their theoretical description requires
highly accurate quantum chemical calculations, which are computationally
expensive. In this review, we focus on not only how machine learning
is employed to speed up such excited-state simulations but also how
this branch of artificial intelligence can be used to advance this
exciting research field in all its aspects. Discussed applications
of machine learning for excited states include excited-state dynamics
simulations, static calculations of absorption spectra, as well as
many others. In order to put these studies into context, we discuss
the promises and pitfalls of the involved machine learning techniques.
Since the latter are mostly based on quantum chemistry calculations,
we also provide a short introduction into excited-state electronic
structure methods and approaches for nonadiabatic dynamics simulations
and describe tricks and problems when using them in machine learning
for excited states of molecules.