The team of researchers on science of science was created by G.M.Dobrov in 1965. Over the following 20 years, Dobrov's team was transferred from one institute to another, unless (in 1986) the Unit for S&T Potential Studies was created, which later (after the death of Dobrov) became G.M.Dobrov Center for Science & Technology Potential and Science History Studies (STEPS Center) of the National Academy of Sciences of Ukraine. The article contains a detailed analysis of scientific achievements by Dobrov and the STEPS Center. Dobrov and his team could gain international merit for introduction, elaboration and clear definition of the notions of 'scientific potential' and 'science and technology potential'. Later on, Dobrov's team had to engage in a broad range of themes, to face new challenges. Themes on which the STEPS Center had to focus in various periods covered: historical reconstruction of the development of natural science in Ukraine till 80s, by research field; revision of the chronology of main events in the Academy over 1918-1998, investigation of little known data about national naturalists; phenomenon of 'academic school' and methodologies for its identification; elaboration of the phase dynamics of the scientist's activity; methodology and sociology of science; evaluation of research and innovation potential, science & technology and innovation forecasting for Ukraine; evolution of informatics in Ukraine; personalities in the NAS of Ukraine; scientometrics (publication activity in the NAS; trends in nuclear research, including nuclear energy, on the basis of INIS); international scientific cooperation.