The intergalactic medium (IGM) and circumgalactic medium (CGM) account for the majority of baryonic matter in the universe -- they provide the vast reservoir upon which galaxies draw during their formation. The cosmic ionizing radiation background shapes the ionization and thermal states of the IGM and CGM. A detailed understanding of this background is therefore crucial for understanding the galaxy formation process and reionization. I will present models of the UV/soft X-ray background and its impact on the IGM and CGM. As I present these models, I will discuss the physics that shapes the background, as well as the current status of observational measurements.