This article discusses how museum settings can provide opportunities for sensory and aesthetic encounters and learning. It draws on research into museum education programmes that included examinations of curatorial construction and display, observations of teaching and open-ended interviews with museum educators. The examples selected here focus on themes of display and learning to illustrate how aesthetic experiences can emerge as incidental adjuncts to learning in other fields. They also acknowledge how museums draw on aesthetic judgements to categorise or present objects and employ aesthetic artefacts and practices as representative devices of cultural engagement, especially in learning themes in the humanities. The studies show how museums can offer opportunities and skills, and cultivate dispositions to the examination of challenging ideas about aesthetic status, sensibility, interpretation or value. Examples of purposefully constructed sites for aesthetic learning show how museum educators have rethought ways of facilitating affective sensory experiences, and raising questions of aesthetic status, response and the social and cultural functions of the arts. The studies discussed here suggest that museums can provide dedicated opportunities to cultivate independent aesthetic thinking and debate about aesthetic ideas as lifelong skills and pleasures.