This thesis investigates the relationship between object-oriented programming languages and game models of computation. These are intuitively well matched: an object encapsulates some internal state and presents some behaviour to the world via its publicly visible methods, while a strategy for some game represents the possible interactions of a program with its environment. We work with a simple and well-understood game model. Rather than tailoring our model to match some existing programming language, we view the simplicity of our semantic setting as a virtue, and try to find the appropriate language corresponding to the model. We define a class-based, stateful object-oriented language, and give a heapbased operational semantics and an interpretation in our game model. At the heart of this interpretation lies a novel semantic treatment of the phenomenon of data abstraction. The model closely guides the design of our language, which enjoys an intermediate level of expressivity between that of first-order and general higher-order store. The agreement between the operational and game interpretations is verified by a soundness proof. This involves the development of specialised techniques and a detailed analysis of the relationship between the concrete and abstract views. We also show that definability and full abstraction hold at certain types of arbitrary rank, but are problematic at other types. We conclude by briefly discussing an extended language with a control operator, along with other extensions leading to a possible core for a more realistic programming language.