Rapid growth of University Mathematics Education (UME) research in the last 40 years – including specialist conferences, journals and books – signals a trajectory away from the margins of Mathematics Education research, nationally and internationally. This growth is reflected well in the number and range of British Society for Research into Learning Mathematics (BSRLM) Proceedings papers too as well as the UME related BSRLM Working Groups over the years. Furthermore, UK-based UME research has been growing steadily and alongside international developments in this area (typically reported in the INDRUM conferences since 2016, the RUME conferences in the US since 2002, the southern-hemisphere focused Delta conferences since 1997 and UME-focused publication outlets such as IJRUME, TMA and PRIMUS). This chapter consolidates forty years of works (1985-2025) presented at BSRLM Day Conferences and aims to be a useful companion alongside the volumes produced by these conferences and journals. 

The range of research topics presented at BSRLM conferences is broad and increasingly diverse. This trajectory is illustrated in the following areas: teaching and learning of specific topics in university mathematics (including calculus, algebra, number theory, discrete mathematics, and proof); mathematics in other disciplines (such as physics, chemistry, biology, engineering and economics); transition to, across and from university mathematics; curricular and institutional issues; novel teaching approaches; digital resources; assessment practices; professional development of university mathematics teachers; and affect, gender, and equity, diversity and inclusion.