Networks have risen to prominence as intellectual technologies and graphical representations, not only in science, but also in journalism, activism, policy, and online visual cultures. Inspired by approaches taking trouble as occasion to (re)consider and reflect on otherwise implicit knowledge practices, in this article we explore how problems with network practices can be taken as invitations to attend to the diverse settings and situations in which network graphs and maps are created and used in society. In doing so, we draw on cases from our research, engagement and teaching activities involving making networks, making sense of networks, making networks public, and making network tools. As a contribution to “critical data practice,” we conclude with some approaches for slowing down and caring for network practices and their associated troubles to elicit a richer picture of what is involved in making networks work as well as reconsidering their role in collective forms of inquiry.