Motivated in part by the missing baryons problem, observers have made substantial efforts in recent years to understand and characterize the complex nature of the intergalactic and circumgalactic media (IGM and CGM). These efforts have led to the realization that the baryon mass contained in the IGM and CGM may be much greater than originally expected and, in the case of the CGM, might contain more than half of all baryonic mass in galactic halos. However, these observations have led to additional questions, some of which may be answered through a deeper understanding of the ionization structure of these media. Furthermore, recent theoretical work suggests that the CGM itself may play a much more significant role in regulating galactic star formation than originally thought. We seek to find answers to these questions through the use of numerical simulations. In particular, I will present some results of my efforts to study the non-equilbrium ionization state of oxygen in the IGM and the overall density and temperature structure of a well-resolved CGM in simulations of isolated galaxies. It is through this numerical work that I hope to help paint a more accurate picture of the IGM and CGM.