A crucial but little-explored practice in design anthropology is the crafting of invitations: invitations to user studies, to interviews, to ethnographic fieldwork projects, to co-design workshops, to prototyping and to public engagement events. The reason for issuing these invitations is partly to widen the epistemological community, partly to democratize the development of new designs or technological systems. In this chapter we engage with the politics of inviting by proposing a shift in what we invite to, and when. Rather than inviting stakeholders to participate in design projects before use, we will argue for the value of inviting participants to take part in co-articulations of issues that arise in the course of the ongoing living with technologies. This, we argue, is an important shift, because the issues and potentialities that emerge as things are used can never be fully predicted in a design project, whether by designers or potential users. We have termed this practice of inviting to collaborative formations of issues connected to the ongoing living with technologies designerly public engagements.