The growth in number of students in the UK higher education sector over recent years has included an increase in numbers of students enrolled for research degrees. For the majority of academics working in UK universities, supervision of research students is now an integral part of their academic practice; indeed for many it will be an explicit requirement of their role and clearly identified in the terms and conditions of employment or job description, using phrases such as ‘to supervise research students through to completion’. This chapter provides an introduction to the supervision of research students reading for research degrees of different types, but with an emphasis on the Doctor of Philosophy (Ph.D.) and Master of Philosophy (M.Phil.). It will also have relevance to those supervising similar doctorates with thesis requirements, such as the Doctor of Medicine (MD or MD [Res]) and professional doctorates (e.g. Ed.D.).