The subject of this article is the unprecedented acceleration of many processes in the present-day world as well as the consequences and problems it provokes. As sociologists, like Z. Bauman, A. Giddens, S. Bertman, U. Beck, J. Urry, T.H. Eriksen and others, emphasized, this acceleration is related to such phenomena as globalization, risk, different mobilities, “nowism”, new nomadism, fragmentation of time and space, etc. The author analyzes the present-day acceleration of life as one of the sources of “presentism”, of domination of the present over past and future and absorption of these latter by it; social amnesia; “delocalization” and “detemporalization” of many events and processes; transformation of time in the incoherent episodes one after another; “juvenilization” of society, closely connected with infantilism; voluminous swell of informational rubbish; aggravating problem of the search and selection of necessary information; difficulties in adaptation to the ceaseless acceleration, and so on. All these and other challenges, provoked by uncontrolled acceleration, were tackled by the “Slow Movement” which became widespread around the world. Author considers some aspects of “Slow Movement” which covers today various areas social life, from food and education to religion, science and art. In the end of article the Russian situation with the problems of time, acceleration and deceleration is analyzed.