Magnetic fields are ubiquitous across different physical systems of current interest; from the early Universe, compact astrophysical objects, and heavy-ion collisions to condensed matter systems. A proper treatment of the effects produced by magnetic fields during the dynamical evolution of these systems can help to understand observables that otherwise show puzzling behavior. Furthermore, when these fields are comparable to or stronger than LambdaQCD, they serve as excellent probes to help elucidate the physics of strongly interacting matter under extreme conditions of temperature and density. This work provides a detailed report that contains in-depth analysis and expert insights into the specific topic of the effects of strong magnetic fields on QED and QCD systems. In this sense, the report is intended as a white paper contribution to the field. The subjects developed include the modification of meson static properties such as masses and form factors, the chiral magnetic effect, the description of anomalous transport coefficients, superconductivity in extreme magnetic fields, the properties of neutron stars, the evolution of heavy-ion collisions, as well as effects on the QCD phase diagram. We describe recent theory and phenomenological developments using effective models as well as LQCD methods. The work was motivated by presentations and discussions during the "Workshop on Strongly Interacting Matter in Strong Electromagnetic Fields" that took place in the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) in the city of Trento, Italy, September 25-29, 2023.
