The essay aims to analyse why the question of ‘acceleration’ has acquired a problematising mood, in the Foucauldian sense, in our contemporary times, and why a connection between ‘acceleration’, the ‘end of History’ and the ‘de-futurisation of the future’ can be found and be functional to the reproduction ofthe form of life of neo-liberal capitalism. The analysis starts with a discussion of the philosophy of the accelerationism and Hartmut Rosa's social philosophy of acceleration, and then moves on to the way in which the Anthropocene – the age of the unfolding ecological crisis, in its connection with all other crises of contemporaneity (economic, social, political, of the human condition) – questions the criteria with which Modernity has thought and thinks about its historical and temporal experience and structures. Drawing on the analyses of Reinhart Koselleck, Niklas Luhmann and Hans Blumenberg – how the temporal structures of Modernity were constructed, why the future cannot begin and the reasons for today's disorientation – the essay aims to understand the possibilities of another way of thinking about historical and temporal experience, something like a revolution of time itself.