The investigations on the history of astronomy proceed rapidly and concern all branches, viz. the history of astronomy in particular countries, the historical development of the astronomical problems, biographies of astronomers, history of observatories and of astronomical instruments etc. They are being made by professional astronomers and historians of science at observatories and institutions destined for the history of science. The president of Commission 41 cannot give a comprehensive review of all directions of investigations on the history of astronomy, because their results frequently have been published in publications not accessible to the author of this report. The present draft report is based mainly on information received by the president from members and consulting members. Besides, the present report contains short information on the results of international conferences, which were held independently of IAU.