In this seminar, I will explore issues around teaching problem solving in mathematics. I will examine different ways in which the term ‘problem solving’ can be understood and suggest a framework for thinking about it. Problem solving is often felt to be conspicuous by its absence from much undergraduate mathematics. I will suggest an approach to teaching problem solving that focuses on the systematic and explicit teaching of specific, carefully-chosen problem-solving tactics, as opposed to more widely applicable generic strategies. I hope that colleagues will be willing to share their thoughts and experiences.