Global health’s ethic of action is based on the assumption of the absence of functioning health care — i.e. public hospitals, health infrastructure and/or expertise — in spaces where it is most active. Yet, myriads of public hospitals exist or remain in global health’s sites of intervention. This chapter addresses this tension. State-run hospitals stand as paradoxical objects of mistrust and investment: they are bypassed and criticized on the grounds of inefficiency but are nonetheless continuously funded and invested with social and political value. In other words, hospitals remain important but often non-acknowledged loci of care, training and research and sites of larger processes of health globalization. This status places them at a central position within the arena of global health. In this chapter, we ask, how novel diseases, techniques and tools are entering these hospitals, and how does global health change the hospital as a site of care (affecting — or not — its infrastructure, human resources, supply chains and position in the health system). In order to do so, we examine three hospitals in East Africa, the Middle-East and Asia, under the light of three globalized domains of health: medical genetics, tuberculosis and mental health. The chapter discusses how these hospitals are massive and complex infrastructures both in the sense that they remain crucial nodes in the health system and that they are complex material organizations whose activity implies multiple layers of logistics. We also show how hospitals figure prominently in the arenas of health globalization while being strongly impacted by the very same processes. Global health as we know it would not exist without hospitals and their recent transformation. However, a remaining feature of public hospitals (globalized or not) is facing scarcity and the necessity to engage in local, clinical, triage in order to manage its consequences.