Public and private institutions are pursuing the very ambitious goal of landing humans on Mars, and returning them safely to Earth, in the near future. This goal is stimulated by international competition in spacefaring technologies, by the possibility of finding new natural resources, by the promise of groundbreaking scientific findings, and by a drive to expand the frontiers of human presence. However, major challenges remain to be overcome. First, interplanetary travel and a stay on Mars will challenge the psychology and physiology of humans; adequate countermeasures must be searched to ensure the health and wellbeing of astronauts. Then, a number of new technologies (heavy launch vehicles, nuclear propulsion vehicles, landing and ascending vehicles, radiation shielding, materials processing, life-support systems) require extensive development. These various requirements, together with high mission costs, render the first crewed missions to Mars challenging in their technical, economic, medical, and ethical aspects.