In this chapter we explore the potential advantages of modeling the interaction between a human and a computer as a consequence of a Partially Observable Markov Decision Process (POMDP) that models human cognition. POMDPs can be used to model human perceptual mechanisms, such as human vision, as partial (uncertain) observers of a hidden state are possible. In general, POMDPs permit a rigorous definition of interaction as the outcome of a reward maximizing stochastic sequential decision processes. They have been shown to explain interaction between a human and an environment in a range of scenarios, including visual search, interactive search and sense-making. The chapter uses these scenarios to illustrate the explanatory power of POMDPs in HCI. It also shows that POMDPs embrace the embodied, ecological and adaptive nature of human interaction.