Mathematics teacher educators are involved with the learning of teachers, of prospective teachers and of themselves. In this chapter, we engage with the question of what theoretical perspectives on learning they use in their published papers. In the process, we offer a theoretical framework for analysing mathematics teacher education and professional development that begins with the interactive website, Discourses on Learning in Education (learningdiscourses.com). We illustrate how the analysis works through two contrasting case studies: Variation Theory and Professional Learning Community. These cases were drawn from proceedings of the 10th Congress of the European Society for Research in Mathematics Education (CERME10), the most recent ERME conference for which papers were available at the time of writing.