A deep space radiation environment of galactic cosmic rays and energetic particles from solar flares imposes stringent requirements for radiation shielding for both personnel and electronic equipment at a moon base or on a Mars expedition. Current Los Alamos capabilities for calculating the effect of such shielding are described, and extensions and validation needed before actual manned deep space missions are launched are outlined. The biological effects of exposure to cosmic-ray ions and to low doses of radiation at low dose rates are poorly understood. Recent Los Alamos work on mutation effects in cells, DNA repair processes, and the analysis of chromosomal aberrations promises to increase our understanding of the basic processes, to provide methods to screen for radiation sensitivity, and to provide advanced dosimetry equipment for space missions.