Gaze shifts in humans serve to direct high-resolution vision provided by the fovea towards areas in the environment. Gaze can be considered a proxy for attention or indicator of the relative importance of different parts of the environment. In this talk, we discuss the development of generative models of human gaze in response to visual input. We discuss how such models can be learned, both using supervised learning and using implicit feedback as an agent interacts with the environment, the latter being more plausible in biological agents. We also discuss two ways such models can be used. First, they can be used to improve the performance of artificial autonomous systems, in applications such as autonomous navigation. Second, because these models are contingent on the human’s task, goals, and/or state in the context of the environment, observations of gaze can be used to infer information about user intent. This information can be used to improve human-machine and human robot interaction, by making interfaces more anticipative. We discuss example applications in gaze-typing, robotic tele-operation and human-robot interaction.