The current status of explanation worked out by Physics for the Periodic Law is considered from philosophical and methodological points of view. The principle gnosiological role of approximations and models in providing interpretation for complicated systems is emphasized. The achievements, deficiencies and perspectives of the existing quantum mechanical interpretation of the Periodic Table are discussed. The mainstream ab initio theory is based on analysis of selfconsistent one-electron effective potential. Alternative approaches employing symmetry considerations and applying group theory usually require some (...) empirical information. The approximate dynamic symmetry of one-electron potential casts light on the secondary periodicity phenomenon. The periodicity patterns found in various multiparticle systems (atoms in special situations, atomic nuclei, clusters, particles in the traps, etc) comprise a field for comparative study of the Periodic Laws found in nature. (shrink)