Astronauts in space are subject to a continuous bombardment of ionizing radiation. The Earth's magnetic field and the ISS shield some biologically damaging particles traveling through. Still, travel beyond low-Earth orbit and extravehicular activities are exceedingly more dangerous and there is a concern for the acute and late-occurring adverse health effects befalling astronauts. So, it is vital to consider the current tools and models used to describe and study the organic consequences of ionizing radiation exposure. It is equally important to see where these models may improve. This article reviews the historical development and current state of knowledge of radiation effects impacting astronauts in orbit. We explain the space radiation environment, cellular microenvironment, and how these may be incorporated in radiobiological models to aid in our understanding of the influence space travel may have on astronaut health. The topics discussed in this paper include a review of DNA damage and repair mechanisms and the numerical models that aim to explain the biological effects resulting from ionizing radiation damage. Historically, radiobiological models focused on how radiation damages nuclear DNA, built upon the hypotheses of Crowther and Lea in the 1940s and 1960s, and neglected other sub-cellular targets outside of nuclear DNA.