The term “Remote Health Care” (RHC) more clearly defines what is implied by Telehealth or Telemedicine. The latter terms clearly indicate delivering health care at a distance using Information and Communication Technology. Distance today has become meaningless–at least on earth ! Geography has indeed become History. The ultimate in providing RHC would be to continuously monitor in almost real time, various health parameters of those in outer space, staying in Low Earth Orbit at present. Eventually this would extend to the lunar surface, deep space and one day perhaps even on the red planet Mars. This overview discusses some of these challenges.