This introduction to the special issue takes as its point of departure three centres of gravity that have shaped the study of neoliberalism but have also established barriers to further progress in these debates. By promoting an intersectional materialist research agenda which challenges extant ideational, modernist and empiricist tendencies in scholarship on neoliberalism, the essay contextualizes the special issue articles by outlining and clarifying key aspects of our understanding of authoritarian neoliberalism. In particular, we reflect on themes related to conceptualization and periodization, which are of importance for both this special issue but also for broader questions of knowledge production and praxis. Through doing so, we argue that there are two distinct yet connected trajectories within the research agenda on authoritarian neoliberalism: one which focuses on the intertwinement of authoritarian statisms and neoliberal reforms; and another which traces various lineages of transformation of key societal sites in capitalism (e.g. states, households, workplaces, urban spaces). Recognition of this spectrum of authoritarian neoliberal practices is important as it helps us uncover how inequalities of power are produced and reproduced in capitalist societies, and pushes us to consider more fully how other worlds can be made possible. Nevertheless, it is affirmed that we must remain open to what an emancipatory society might look like, and what struggles would be most appropriate, in and across various socio-spatial contexts.