The effects of the space radiation environment on spacecraft systems and instruments are significant design considerations for space missions. Astronaut exposure is a serious concern for manned missions. In order to meet these challenges and have reliable, cost-effective designs, the radiation environment must be understood and accurately modeled. The nature of the environment varies greatly between low earth orbits and higher earth orbits. There are both short-term and long-term variations with the phase of the solar cycle. In this paper we concentrate mainly on charged particle radiations in the near-Earth region. Descriptions of the radiation belts and particles of solar and cosmic origin are reviewed. An overview of the traditional models is presented accompanied by their application areas and limitations. This is followed by discussion of some recent model developments.