This review provides a comprehensive summary of lattice QCD simulations that investigate the physics of strongly interacting matter in the presence of background electromagnetic fields. The field has evolved into an independent research direction, driven by landmark results on the phase diagram, equation of state, confinement mechanism, and anomalous transport phenomena. The review covers various aspects, including the impact of magnetic and electric fields on hadron properties, the deconfinement transition, the equation of state, and transport phenomena. It also discusses the renormalization of observables and the challenges posed by background fields, such as flux quantization and twisted boundary conditions. The review aims to provide a self-contained overview for a broad audience interested in strongly interacting matter under extreme conditions, highlighting key lessons and open questions in the field.This review provides a comprehensive summary of lattice QCD simulations that investigate the physics of strongly interacting matter in the presence of background electromagnetic fields. The field has evolved into an independent research direction, driven by landmark results on the phase diagram, equation of state, confinement mechanism, and anomalous transport phenomena. The review covers various aspects, including the impact of magnetic and electric fields on hadron properties, the deconfinement transition, the equation of state, and transport phenomena. It also discusses the renormalization of observables and the challenges posed by background fields, such as flux quantization and twisted boundary conditions. The review aims to provide a self-contained overview for a broad audience interested in strongly interacting matter under extreme conditions, highlighting key lessons and open questions in the field.