This paper presents a general decision theoretic model of interactions between users and cognitive assistive technologies for various tasks of importance to the el- derly population. The model is a partially observable Markov decision process (POMDP) whose goal is to work in conjunction with a user towards the comple- tion of a given activity or task. This requires the model to monitor and assist the user, to maintain indicators of overall user health, and to adapt to changes. The key strengths of the POMDP model are that it is able to deal with uncertainty, it is easy to specify, it can be ap- plied to different tasks with little modification, and it is able to learn and adapt to changing tasks and situations. This paper describes the model, gives a general learn- ing method which enables the model to be learned from partially labeled data, and shows how the model can be applied within our research program on technologies for wellness. In particular, we show how the model is used in three tasks: assisted handwashing, health and safety monitoring, and wheelchair mobility. The paper gives an overview of ongoing work into each of these areas, and discusses future directions.