This chapter relies on a panel at INDRUM 2 in Kristiansand (Norway) that focused on education and professional development of university mathematics teachers and set out from recognising that university mathematics teaching today must address the needs of highly varied student cohorts – in terms of background and specialism – and that it does so in a highly potent digital learning environment. Thinking more systematically about the professional preparation and development of university mathematics teachers (UMTE) includes presenting current practices (with examples from the UK, USA, Germany and Norway) and proposing new ideas for discipline and context-specific teacher preparation and for identifying and rewarding quality teaching.