In this chapter, we provide an overview of the principles of active inference. We illustrate how different forms of short-term memory are expressed formally (mathematically) through appealing to beliefs about the causes of our sensations and about the actions we pursue. This is used to motivate an approach to active vision that depends upon inferences about the causes of 'what I have seen' and learning about 'what I would see if I were to look there'. The former could manifest as persistent 'delay-period' activity - of the sort associated with working memory, while the latter is better suited to changes in synaptic efficacy - of the sort that underlies short-term learning and adaptation. We review formulations of these ideas in terms of active inference, their role in directing visual exploration and the consequences - for active vision - of their failures. To illustrate the latter, we draw upon some of our recent work on the computational anatomy of visual neglect.