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 photoexcitations. One can thus expect the emergence of interesting nonlinear responses, transient states, and photoinduced phases in Mott systems. This review provides a comprehensive overview of the current understanding of photoexcited Mott insulators by discussing excitation protocols, nonlinear optical responses, the underlying mechanisms governing photocarrier dynamics, and the pathways leading to photoinduced metastable states. The review focuses on recent theoretical progress, identifies the relevant underlying concepts, and links them to experimental observations. The review starts with a general discussion of field-induced nonequilibrium setups and an overview of key experiments that revealed characteristic properties of photoexcited Mott states, proceeds with an overview of the theoretical tools that 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. The appearance of nonthermal electronic orders in photoexcited Mott systems, including nonthermal spin and orbital orders, $\eta$-pairing states, and novel types of excitonic orders, is also discussed.

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• Light-matter interaction
• Photoinduced effect
• Mott insulators
• Nonequilibrium systems
• Strongly correlated systems