The observational study of galaxy cluster outskirts is a new territory to probe the thermodynamic and chemical structure of the X-ray emitting intracluster medium (ICM). Cluster outskirts are particularly important for modeling the Sunyaev-Zel'dovich effect, which is sensitive to hot electrons at all radii and has been used to detect hundreds of galaxy clusters with recent microwave cluster surveys. In cluster-based cosmology, measurements of cluster outskirts are an important avenue for estimating the cluster mass, as the outskirts are less sensitive to baryonic processes that dominate the cluster core. However, recent observations of cluster outskirts deviate from theoretical expectations, indicating that cluster outskirts are more complicated than previously thought. Computational modeling of cluster outskirts is necessary to interpret these observations. I will present cosmological simulations of galaxy cluster formation that follow the thermodynamic and chemical structures in the virialization regions of the ICM and transition to the IGM. Specifically, I will discuss how observational signatures of galaxy clusters are affected by gas flows, inhomogeneities in the ICM, and non-equilibrium physics.