Much research into postgraduate student learning focuses on generic issues of research development. Early work, reported here, uses threshold concept theories and theories of conceptual threshold crossing to focus on the learning and supervisory support of postgraduates researching in the fields of literature and art. This paper is based on interviews with postgraduate students, postdoctorates and supervisors. It considers effective practices supporting postgraduate students and explores the reporting of experience, textual examples and dialogues to determine some of the characteristics in practice of both bringing threshold concepts into play in students' research and supporting their crossing of conceptual thresholds. We argue that identifying and working towards the overcoming of blockages or "stuck places" in research can lead to conceptualised, critical and creative work in literature and art PhDs.