Many space advocates would like to see permanent human settlements on the Moon and Mars. However, no one knows if it is possible to live healthfully for long periods of time in gravity that is 16% (Moon) or 38% (Mars) of what we experience here on the surface of earth.
The following video from the Space Studies Institute (SSI) shows a talk given by Gary Hudson at the Space Access Society‘s annual meeting last May in which he discussed the need to do partial gravity studies in orbit to investigate partial gravity questions. He discusses SSI’s proposed G-Lab, a facility in earth orbit that would rotate at different rates so as to generate artificial spin-gravity at levels of interest for animal and human studies: SSI G-Lab at Space Access 2015 – Space Studies Institute
If Mars gravity isn’t sufficient to support a long healthy life, that does not mean we cannot live in space. Large in-space settlements can produce 1g via rotation: