Theoretical and experimental studies of the interaction between atoms and molecules chemisorbed on the surface of a metal are described. The basic interaction mechanisms are studied theoretically: 1) direct--owing to the direct exchange of electrons between adatoms; 2) indirect--owing to the exchange of electrons through the conduction band of the metal substrate; and, 3) electrostatic--owing to the exchange of photons and surface plasmons between charged adatoms. Experimental studies performed with a field-ion microscope and by the LEED technique are described in detail. The two-dimensional adatom structures observed on the channeled faces of transition metals enable studying the interaction at record large distances (up to 25 $\mathring{\mathrm{A}}$). The following are studied briefly: the interaction of adatoms on a semiconductor surface, interaction-induced restructuring in an adsorbed atomic film, reconstruction of clean metal and semiconductor surfaces, and other manifestations of interaction in adsorption systems.