In the demographic changes that Homo sapiens have suffered during the last 250,000 years, a law has always governed: grow, stagnate and decrease. During the last centuries, and thanks to fossil fuels like oil, our civilization has grown like never before. In 200 years the number of inhabitants has multiplied by ten and by almost twenty the consumption of energy per capita. The cost we pay for this is too high: the stability of the Earth is in grave danger. Is it possible to achieve sustainable development? Do we have to limit growth? Expansions and withdrawals invites us on a journey through the population history of our species, searching for solutions to this great challenge that humanity faces.