Topical problems of domestic and foreign science studies associated with the contradictions in evaluating the contribution of domestic scientists to the world science are considered. The erroneousness of the approaches caused by the priority evaluation of the scientific activity effectiveness of Russian scientists based on using international scientometric ratings and databases is shown. The main tools of traditional scientometrics are presented, methodological approaches to determining the researchers’ ratings based on scientometric indicators are shown. Various options for modifying the calculations of the Hirsch index values for different numbers of publications are described. It is shown that, on the basis of the considered indices, it becomes possible to evaluate a scientist’s publication activity by three ratings, namely: rating of significant works; rating of work intensity; a complex rating, including both ones. When establishing a rating, it is advisable to give preference to the index of basic publications. As a result of a comparative analysis of domestic and foreign studies, it is revealed that scientometrics is a real tool for analyzing and evaluating scientists’ activities, scientific organizations and educational institutions.