  This is an introductory review of lattice QCD with external fields. The study
of external magnetic fields is one of the greatest achievements in modern
lattice QCD. Large-scale simulations and detailed analyses have revealed
intriguing properties of QCD in the magnetic fields. The study of external
electric fields is more challenging because of a technical difficulty. We
overview the successes and challenges of the lattice simulations with the
electromagnetic fields. We also introduce a newly developing field, the lattice
simulation of rotating QCD matters.
