This chapter articulates the central challenge to the project of conceptual engineering, which is called the Strawsonian Challenge. The central idea is that if conceptual engineering involves changing the extensions and intensions of our terms, then a successful change of meaning will not give us a better way to talk about the issues and questions we were concerned with; rather it will simply change the topic. This challenge was first articulated in Strawson’s response to Carnap’s project of explication, but reoccurs throughout work on conceptual engineering in various different forms. The chapter articulates various different forms of this challenge, and previews the author’s responses to them.