Improving teacher design promises to be a scalable, sustainable approach to building capacity amongst a workforce faced with complex and evolving drivers of change in higher education worldwide. While design has long been recognised as a routine part of teaching, there has been renewed interest in supporting and understanding the design work that teachers do to foster innovation, particularly in technology-enhanced learning, at institutional scale by influencing teachers' practices. Re-framing teaching as design usefully emphasises the creative problem-solving needed to balance pedagogical, logistical and technical considerations within specific educational contexts, tailored to learners' needs. There is potential for this re-framing to build on and advance work in "learning design" and "design for learning" that has generated a wide range of practical supports and tools. In this article, we explore, problematise and conceptualise the notion of "teacher as designer" within the complexity of contemporary higher education through a critical review of existing empirical and conceptual work internationally. We offer insights into the current state of knowledge about teacher design in higher education, highlight gaps and possibilities, offer a new conceptualisation drawing on practice theory and set out propositions to provoke further debate about teacher design as a vehicle for sustainable innovation in higher education.