  We provide a pedagogical review article on fundamentals and applications of
the quantum dynamics in strong electromagnetic fields in QED and QCD. The
fundamentals include the basic picture of the Landau quantization and the
resummation techniques applied to the class of higher-order diagrams that are
enhanced by large magnitudes of the external fields. We then discuss observable
effects of the vacuum fluctuations in the presence of the strong fields, which
consist of the interdisciplinary research field of nonlinear QED. We also
discuss extensions of the Heisenberg-Euler effective theory to finite
temperature/density and to non-Abelian theories with some applications. Next,
we proceed to the paradigm of the dimensional reduction emerging in the
low-energy dynamics in the strong magnetic fields. The mechanisms of
superconductivity, the magnetic catalysis of the chiral symmetry breaking, and
the Kondo effect are addressed from a unified point of view in terms of the
renormalization-group method. We provide an up-to-date summary of the lattice
QCD simulations in magnetic fields for the chiral symmetry breaking and the
related topics as of the end of 2022. Finally, we discuss novel transport
phenomena induced by chiral anomaly and the axial-charge dynamics. Those
discussions are supported by a number of appendices.
