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The space radiation environment is a complex mixture of particle types and energies originating from sources inside and outside of the galaxy. These environments may be modified by the heliospheric and geomagnetic conditions as well as planetary bodies and vehicle or habitat mass shielding. In low Earth orbit (LEO), the geomagnetic field deflects a portion of the galactic cosmic rays (GCR) and all but the most intense solar particle events (SPE). There are also dynamic belts of trapped electrons and protons with low to medium energy and intense particle count rates. In deep space, the GCR exposure is more severe than in LEO and varies inversely with solar activity. Unpredictable solar storms also present an acute risk to astronauts if adequate shielding is not provided. Near planetary surfaces such as the Earth, moon or Mars, secondary particles are produced when the ambient deep space radiation environment interacts with these surfaces and/or atmospheres. These secondary particles further complicate the local radiation environment and modify the associated health risks. Characterizing the radiation fields in this vast array of scenarios and environments is a challenging task and is currently accomplished with a combination of computational models and dosimetry. The computational tools include models for the ambient space radiation environment, mass shielding geometry, and atomic and nuclear interaction parameters. These models are then coupled to a radiation transport code to describe the radiation field at the location of interest within a vehicle or habitat. Many new advances in these models have been made in the last decade, and the present review article focuses on the progress and contributions made by workers and collaborators at NASA Langley Research Center in the same time frame. Although great progress has been made, and models continue to improve, significant gaps remain and are discussed in the context of planned future missions. Of particular interest is the juxtaposition of various review committee findings regarding the accuracy and gaps of combined space radiation environment, physics, and transport models with the progress achieved over the past decade. While current models are now fully capable of characterizing radiation environments in the broad range of forecasted mission scenarios, it should be remembered that uncertainties still remain and need to be addressed.