In this talk, I will reflect on mathematics teacher education for secondary and elementary schools, drawing on my experience in leading programs for both pre-service and in-service education. The talk also draws on a major literature review which I recently completed for the forthcoming Handbook of Mathematics Teacher Education from Sense Publications. I will discuss four components of mathematics for teaching: knowledge of the content of mathematics; experience of doing mathematics; knowledge about mathematics as a discipline; and knowing how to learn mathematics. Teachers also need pedagogical content knowledge, a special blend of knowledge of mathematics and pedagogy that is uniquely required by the teaching task. Research generally shows only weak links between university studies of mathematics and effectiveness as a teacher, so the challenge is to provide teacher education which really makes a difference to student learning. These ideas will be discussed with regard to current circumstances in Australia, when qualified mathematics teachers are in short supply (as in many Western countries) and when school systems are increasing emphasis on improving student outcomes.