In philosophy, the term "modality" refers to the different ways or modes in which things could be. Some things are necessary, some things are possible, and some things are impossible. There are also different kinds of possibility. Some things are physically possible but biologically impossible, for instance, or logically possible but physically impossible. Understanding the boundaries between what is necessary, possible, and impossible is a difficult task, and a large number of logicians, metaphysicians and epistemologists have endeavored their whole careers to clarify this difficult issue. In this talk, I hope to show that cognitive psychology and neuroscience can contribute to this ongoing and fascinating research by uncovering the neural and cognitive mechanisms underlying certain kinds of modal judgments. In particular, I hope to show that thoughts about alternative ways in which the past could, should, or would have been, draw resources from different memory systems depending on certain features of the counterfactual content, such as the perceived likelihood of the counterfactual event, or whether or not the counterfactual event involves a person one is familiar with. My hope is to show that modal cognition is a promising and highly interdisciplinary area of research in cognitive neurophilosophy.