This chapter discusses social norms with attention to their significance for researching and designing digital touch communication in a global world, notably gendered and cultural touch norms. It explores how social and cultural norms shape the ways that people (and machines) touch. Touch norms are shaped, regulated and enforced through social, economic, familial and legal mechanisms, they organise our experiences and expectations. Understanding of the touch norms that people, including digital touch researchers and designers, bring to their interactions with others provides a route into understanding the sociality that shapes digital touch. We discuss the significance of these given the expectations of the user, their touch repertoires, and the social cultural role that norms play in the take up and use of mediated digital touch communication devices and systems and environments. The chapter concludes that reflexive engagement with touch norms can provide insights and inspiration for thinking about, researching and designing digital touch communication, and help to address how cultural and gendered norms of touch might be engaged with, to constrain and reproduce or open-up the meaning potentials of digital touch.