Zeeman's discovery of the splitting of atomic spectral lines in a magnetic field marked the beginning of studies of the magnetic properties of atoms and molecules
The role of the interaction of molecular systems with a magnetic field is most clearly manifested in astronomy, the theoretical description of objects of which often naturally includes magnetohydrodynamic kinetic equations describing the behavior of cold interstellar plasma, the dynamics of stars and planetary ionospheres, as well as matter near compact objects: white dwarfs, magnetars, and neutron stars.

Accounting for the quantum effects of the interaction of matter with a magnetic field is necessary to correctly describe the dynamics of stellar evolution, the spectra of interstellar gas (in applications to which the Zeeman splitting associated with the hyperfine structure of molecular hydrogen was first detected for the Milky Way), and the formation molecules in interstellar space and binary systems.
Finally, the matter near compact objects is subject to both appreciable GR effects and superstrong magnetic fields: for white dwarfs 10^{6}–10^{6}G, neutron stars 10^{13}G), and for first theoretically predicted, and then experimentally discovered magnetars 10^{15}G.

In view of the fact that fields with strengths up to 107 G can currently be recreated under terrestrial conditions, the latest astronomical objects provide what can be called a natural physical experiment. The correlation and prediction of the spectra corresponding to these objects require theoretical approaches applicable to relativistic quantum dynamics in the asymptotics of strong electromagnetic fields.
In particular, the creation and testing of such methods is of interest from the point of view of molecular physics, in whose optics the joint allowance for relativistic/quantum electrodynamic effects for strong magnetic fields can lead to new results that would otherwise be difficult to predict even at a qualitative level.

The report discusses the features of the relativistic and conventional quantum description of one-electron systems, gives general QED expressions, considers the relativistic hydrogen atom, reviews the classical problems of motion in a Coulomb or magnetic field in the relativistic and nonrelativistic cases, and gives QED corrections to two-particle interaction. Approaches to solving the problem of an electron in a uniform magnetic field and the Coulomb field are also presented. The results of modeling the electronic states of atoms of the second period in uniform external strong magnetic fields, obtained by modifying the single-particle part of the electron Hamiltonian, are presented. A comparative analysis of the current state of affairs in this area is given.

The author is grateful to the Russian Science Foundation for the financial support under Project 22-23-01180.