Many atomic systems exhibit indications of compressed electronic shell: atoms locked in crystals, solids at cryogenic temperatures, atoms trapped by fullerene cages, and atoms in substances under high pressure. This paper collects available experimental data on the ESR, NMR, and magnetic moments of compressed atoms and formulates some general trends in the behavior of magnetic parameters displayed by compressed atoms. The paper lays special emphasis on the electron-nuclear (hyperfine) coupling as a parameter characterizing the modification of atomic orbitals and the redistribution of; spin density in atoms under compression.