The present era is characterized by scientists' high level of mobility, which is due to the characteristics of science work and its dynamic nature. Scientific activity knows no boundaries, and mobility is a vital factor of the mutual cultural and professional enrichment of scientific communities. The international migration of scientists is creating opportunities and challenges for societies that both lose and gain scientists. In this article, the author describes the types of scientists' social mobility and discusses the state regulation of the social mobility of scientists in Russia, Western Europe, and the United States. The author also identifies negative consequences of scientists' social mobility in these countries. The high level of scientists' international mobility has introduced serious changes in the mechanism of the reproduction of the scientific elite in Russia. Owing to the emigration character of mobility and the lack of an appropriate science policy, Russia is lagging behind the developed countries of Europe and the United States when it comes to indicators of its inclusion in the world science community. Here, the author argues that more attention needs to be given by the Russian government to the development of programs and organizations that would enable Russian science to be more competitive internationally.