The orbitofrontal cortex (OFC) is important in processing rewards and other behavioral outcomes. Here, we review from a computational perspective recent progress in understanding this complex function. OFC neurons appear to represent abstract outcome values, which may facilitate the comparison of options, as well as concrete outcome attributes, such as flavor or location, which may enable predictive cues to access current outcome values in the face of dynamic modulation by internal state, context and learning. OFC can use reinforcement learning to generate outcome predictions; it can also generate outcome predictions using other mechanisms, including the evaluation of decision confidence or uncertainty. OFC neurons encode not only the mean expected outcome but also the variance, consistent with the idea that OFC uses a probabilistic population code to represent outcomes. We suggest that further attention to the nature of its representations and algorithms will be critical to further elucidating OFC function.