Humans are the most adaptable species on this planet, able to live in vastly different environments on Earth. Space represents the ultimate frontier and a true challenge to human adaptive capabilities. As a group, astronauts and cosmonauts are selected for their ability to work in the highly perilous environment of space, giving their best. Terrestrial research has shown that human cognitive and perceptual motor performances deteriorate under stress. We would expect to observe these effects in space, which currently represents an exceptionally stressful environment for humans. Understanding the neurocognitive and neuropsychological parameters influencing space flight is of high relevance to neuroscientists, as well as psychologists. Many of the environmental characteristics specific to space missions, some of which are also present in space flight simulations, may affect neurocognitive performance. Previous work in space has shown that various psychomotor functions degrade during space flight, including central postural functions, the speed and accuracy of aimed movements, internal timekeeping, attentional processes, sensing of limb position and the central management of concurrent tasks. Other factors that might affect neurocognitive performance in space are illness, injury, toxic exposure, decompression accidents, medication side effects and excessive exposure to radiation. Different tools have been developed to assess and counteract these deficits and problems, including computerized tests and physical exercise devices. It is yet unknown how the brain will adapt to long-term space travel to the asteroids, Mars and beyond. This work represents a comprehensive review of the current knowledge and future challenges of cognitive neuroscience in space from simulations and analog missions to low Earth orbit and beyond.