A fundamental requirement of any autonomous robot system is the ability to predict the affordances of its environment. In this dissertation, we develop a computational model of affordance learning with object categorization where a robot explicitly learns the object categories in a partially supervised manner and conducts experiments on its enviorment to both refine its model of categories and affordances. We demonstrate that compared with the conventional direct perception approach, categories make the affordance learning problem scalable, especially with scare training data and in incremental learning of new affordances. Another key aspect of our approach is to leverage the ability of a robot to perform experiements on its environment and gather information independent of human trainer. We validate our theory on experiements with physically-situated robots. Finally, we refocus the object categorization problem of computer vision back to the robotics workd and extend the Gluck-Corter category utility for the task of affordance prediciton.