The great importance of scientific researches in the modern society clearly explains a significant role of different forms of united societies of scientific leaders. From the Age of Enlightenment in developed countries this gives rise to formation of national academies of sciences. Such kind of academy was organized also in Russia. As a useful illustration of strong and weak qualities of activities of the Russian academy, thehistoric analysis was given, beginning from the times of its formation and in later periods. Closer to the present time, one may compares the activities of The Academy of Sciences of the USSR in the post-war and later times. Especially important was the mobilization period of activity of the Soviet Academy, which is associated with success of atomic and cosmic projects. Unfortunately, later there was a period of bureaucratic forms of management. It became clear that the Academy needs in significant reforms.The significant progress was achieved only in the twentieth century. The Academy acquired some independence, there was an essential increasing in number of its members, the network of academic research institutes was organized and extended. A significant part of research were performed on the modern level. The big loss in conditions (especially financing) for researches in Russian academic instituteswas observed in post-soviet 1990-ies. In spite of some positive changes (grant financing, extension of international scientific contacts) scientific researches in Russia in the 21st century are still behind in level of developed countries. And again it is necessary to insist in necessity of essential reforms which should be elaborated with obligatory involvement of the most qualified and responsible scientists including leading Russian scientists working in the top foreign research institutes.