Exploding stars have long been considered a threat to life on Earth. While early studies were speculative, modern research is based on advanced observations, theory, and modeling. This review examines supernova explosions, γ-ray bursts (GRBs), and kilonova outbursts, which are major sources of ionizing radiation in galaxies. This radiation can harm Earth-like biospheres by destroying stratospheric ozone, increasing exposure to solar ultraviolet radiation, and producing cosmic-ray muons that penetrate belowground and underwater. Using recent work, we calculate rates for nearby explosions based on distance from the Earth and ionizing radiation dose. Over the Earth's history, core-collapse supernova cosmic rays, γ-rays from Type Ia supernovae, X-rays from Type IIn supernovae, and γ-rays from long GRBs have likely caused significant biosphere damage. However, short GRBs and kilonovae are less concerning. Future research could address open questions through nuclear and particle experiments, astronomical observations, and studies in climate, geology, radiation, and evolutionary biology.