Smart phones are now capable of supporting a wide range of applications, many of which demand an ever increasing computational power. This poses a challenge because smart phones are resource-constrained devices with limited computation power, memory, storage, and energy. Fortunately, the cloud computing technology offers virtually unlimited dynamic resources for computation, storage, and service provision. Therefore, researchers envision extending cloud computing services to mobile devices to overcome the smartphones constraints. The challenge in doing so is that the traditional smartphone application models do not support the development of applications that can incorporate cloud computing features and requires specialized mobile cloud application models. This article presents mobile cloud architecture, offloading decision affecting entities, application models classification, the latest mobile cloud application models, their critical analysis and future research directions.