Ionizing radiation is a ubiquitous feature of the Cosmos, from exogenous cosmic rays (CR) to the intrinsic mineral radioactivity of a habitable world, and its influences on the emergence and persistence of life are wide-ranging and profound. Much attention has already been focused on the deleterious effects of ionizing radiation on organisms and the complex molecules of life, but ionizing radiation also performs many crucial functions in the generation of habitable planetary environments and the origins of life. This review surveys the role of CR and mineral radioactivity in star formation, generation of biogenic elements, and the synthesis of organic molecules and driving of prebiotic chemistry. Another major theme is the multiple layers of shielding of planetary surfaces from the flux of cosmic radiation and the various effects on a biosphere of violent but rare astrophysical events such as supernovae and gamma-ray bursts. The influences of CR can also be duplicitous, such as limiting the survival of surface life on Mars while potentially supporting a subsurface biosphere in the ocean of Europa. This review highlights the common thread that ionizing radiation forms between the disparate component disciplines of astrobiology.