The paper focuses on one central point of the ‘performative’ approach to homelessness that is still inadequately explored by the current literature: the conceptualisation of the relational entanglements between homeless people and the city. The argument is that only through a critical attention to these fluid and more-than-human details will we be able to re-imagine a different politics of homelessness. The paper, engaging with the work of Deleuze and Guattari as well as with critical assemblages thinking, proposes two concepts that are considered to be fundamental in this sense. First, assemblage, as a concept able to render the hybrid constituency of the individual within the city; and second, abstract machines, as a way to take into account the fluidity of power in affecting one's own experience of homelessness. The approach proposed in the paper is illustrated through the presentations of original ethnographic material derived from ten months of ethnographic fieldwork in Turin, Italy. The paper concludes by suggesting that the abstract machine of homelessness can be tackled in at least two ways. First, re-working the institutional assemblages of care that produce stigmatising discourses and deep emotional effects. Second, liberating homeless people's capacities and resources, which are currently poorly accounted by canonical literature and policies.