A review of the regularities in various lanthanide and actinide properties considered as functions of atomic number is given. The regularities, which have been called the tetrad or the double-double effect, are due to symmetry of the ∫-shell and can be conveniently depicted with the use of the expression for the ground energy term in the Racah representation. The tetrad effect has its lower and upper boundaries, imposing certain restrictions on the relative changes in the Racah parameters. Since the tetrad effect in stability constants depends on the magnitude of the nephelauxetic effect, the region of the possible relative nephelauxetic changes of Racah parameters is also presented. The regularities serve as a basis for a semiempirical approach for determination of ionic radii, ∫q→∫q-1dtransition energies, oxidation potentials and other properties of the lanthanides and actinides. In connection with the regularities in ∫q→∫q-1dtransition energies and oxidation potentials, the relative stabilities of various valence states of the ∫-elements are considered.