After a brief review of the hierarchical Bayesian viewpoint, I will present examples of interest in the geosciences. The first is a paleoclimate setting. The problem is to use observed temperatures at various depths and the heat equation to infer surface temperature history. The second combines an elementary physical model with observational data in modeling the flow of the Northeast Ice-Stream in Greenland. The next portion of the talk presents ideas and examples for incorporating output from large-scale computer models (e.g., climate system models) into hierarchical Bayesian models.