This article draws together two linked studies on formal teaching spaces within one university. The first consisted of a multi‐method analysis, including observations of four teaching events, interviews with academics and estates staff, analysis of architectural plans, and a talking campus tour. The second study surveyed 166 students about their perceptions of existing teaching spaces and dreams of ideal spaces, eliciting qualitative comments. Researchers used a comparative analysis of the data to generate themes. Academics and students held differing conceptions of space. For students, a functional view prevailed with teacher‐centred and dominant approaches (lectures, seminars, tutorials) constraining their imagination of fresh possibilities. Academics reflected on the limits and potential of spaces, surfacing more abstract concepts about familiarity, invisibility, space–time dimensions, territoriality and collegiality. The article explores the boundaries that space may place over imagined and alternative pedagogies, and concludes that familiar, computer‐networked and conventional spaces may re‐inscribe hierarchical, teacher‐centred approaches.