CARMENES is a radial-velocity survey with the 3.5m telescope on Calar Alto looking for terrestrial planets in the habitable zones of 300 nearby M dwarfs. A consortium of eleven German and Spanish institutions built a pair of stabilized high-resolution spectrographs especially for this project. I will explain the scientific and technical considerations underlying the instrument design, show some early science data, and discuss the astronomy program that will be carried out with CARMENES in the coming years.