Over the last 10-15 years, the study of NIP theories has amplified the significance of probability measures as a tool for understanding definable sets in first-order theories. This talk will focus on the extent to which one can generalize fundamental results about Keisler measures in NIP theories beyond the NIP setting. On one hand, we will encounter the outright failure of basic properties beyond the safe harbor of NIP, which suggests a certain level of bad news for the general study. On the other hand, however, we will find that appropriate generalizations do indeed exist and even provide new conceptual insight into the role of NIP. Ultimately, in both hands, there will be plenty of open questions and possibilities for further investigation.

This is joint work with K. Gannon and J. Hanson.