This paper argues that the acceleration of life rhythms in the contemporary period is exacerbated by new temporal practices related to what we call algorithmic capitalism. We focus on a historical and theoretical analysis of the relationship between leisure time and the market, and the anchoring of lived times to market imperatives. The historical definition of leisure as an “extra-economic” practice, remote from any economic concerns, is now made obsolete by the neoliberal, and then algorithmic, restructuration of capitalism, and especially the valorization of attention time. The article examines these questions, mobilizing and critically engaging with the theory of social acceleration, time studies, and heterodox political economy.