This paper outlines the new opportunities that that will be changing the landscape of geometry education at the primary school level. These include: the research on spatial reasoning and its connection to school mathematics in general and school geometry in particular; the function of drawing in the construction of geometric meaning; the role of digital technologies; the importance of transformational geometry in the curriculum (including symmetry as well as the isometries); and, the possibility of extending primary school geometry from its typical emphasis on vocabulary (naming and sorting shapes by properties) to working on the composing/decomposing, classifying, comparing and mentally manipulating both two- and three-dimensional figures. We discuss these opportunities in the context of historical developments in the nature and relevance of school geometry. The aim is to motivate and connect the set of papers in this special issue.