Future space missions outside the magnetosphere will subject astronauts to a hostile and unfamiliar radiation environment. An annual dose equivalent to the blood-forming organs (BFOs) of approximately 0.5 Sv is expected, mostly from heavy ions in the galactic cosmic radiation. On long-duration missions, an anomalously-large solar energetic particle event may occur. Such an event can expose astronauts to up to approximately 25 Gy (skin dose) and up to approximately 2 Sv (BFO dose) with no shielding. The anticipated radiation exposure may necessitate spacecraft design concessions and some restriction of mission activities. In this paper we discuss our model calculations of radiation doses in several exo-magnetospheric environments. Specific radiation shielding strategies are discussed. A new calculation of aluminum equivalents of potential spacecraft shielding materials demonstrates the importance of low-atomic-mass species for protection from galactic cosmic radiation.