Abstract <p>This paper provides a synoptic review of the cycle of studies performed by a team affiliated with the IPE RAS in order to look for new approaches to problems of earthquake physics. The fundamental Omori, Gutenberg–Richter, and Bath laws invariably served as the basis and guiding light during our research for many years. The concept of a triad of tectonic earthquakes as a natural trinity of foreshocks, main shocks and aftershocks is used in the paper to arrange thematic material. We provide a classification for main shocks as part of six types of triad identified experimentally. We list the parameters involved in the three laws for the different triad types. An axiomatic theory is given to describe aftershock evolution. We define new concepts, viz, source deactivation, Omori epoch, and source bifurcation; as well, we introduce the concept of proper time for nonstationary lithosphere processes. Convergence of foreshocks and divergence of aftershocks are mentioned. The general conclusion runs as follows: the Omori, Gutenberg–Richter, and Bath laws provide a reliable basis for experimental and theoretical study of earthquakes. These laws possess deep content, which made itself felt in the possibility of enriching the original formulations of the first discoverers with interesting and important additional statements</p>