Machines do not think fast and slow in the sense that humans do in dual-process models of cognition. However, the people who create the machines may attempt to emulate or simulate these fast and slow modes of thinking, which will in turn affect the way end users relate to these machines. In this opinion article we consider the complex interplay in the way various stakeholders (engineers, user experience designers, regulators, ethicists, and end users) can be inspired, challenged, or misled by the analogy between the fast and slow thinking of humans and the Fast and Slow Thinking of machines.