This paper considers two strands of research that each contributes to an understanding of touch-based interaction with private and public displays. The first is based on general frameworks for private device–public display interaction, which is driven by the growing body of work in the area, but focuses on the level of integration of public and private devices and the importance of understanding social setting and bystanders. The second strand is centred on physicality; how different kinds of physical device impact interaction and how modelling of touch-based devices causes particular problems that require notations and formalisms of continuous and bodily interaction.