This chapter is based on three components: that critical thinking is foundational to teaching, that it is hard to define and that it is hard to measure. The participants of the author’s research study were split on each issue and their responses are carefully discussed. For those still wishing to teach for critical thinking, the penultimate part of the chapter deals with different approaches to teaching and curriculum design that ought to achieve a level of criticality for students. These are teaching critical thinking (1) as a skill, (2) as a value, (3) through modelling and (4) through learning to do research. The chapter ends with some thoughts about the broader purposes of higher education and why society needs critical thinkers.