  The study of nonequilibrium phenomena in interacting lattice systems can
provide new perspectives on correlation effects, and information on metastable
states of matter. Mott insulators are a promising class of systems for
nonequilibrium studies, since they exhibit exotic phenomena and complex phase
diagrams upon doping, and because a large Mott gap provides protection against
fast thermalization and heating after photo-excitations. We can thus expect the
emergence of interesting transient states and photo-induced phases in Mott
systems. This review presents the current understanding of the mechanisms which
control the time evolution of photo-doped charge carriers and the properties of
photo-induced metastable states. We focus on recent theoretical progress,
identify the relevant underlying concepts, and link them to experimental
observations. The review starts with a general discussion of field-induced
nonequilibrium setups and an overview of key experiments which revealed
characteristic properties of photo-excited Mott states, proceeds with a compact
overview of the theoretical tools which have been developed to investigate
these strongly correlated nonequilibrium states, and then analyzes Mott
insulators driven out of equilibrium by static electric fields, periodic
fields, and short laser pulses. We also discuss the appearance of nonthermal
electronic orders in photo-excited Mott systems, including nonthermal spin and
orbital orders, $\eta$ pairing states, and novel types of excitonic orders.
