Conversation Analysis (CA) tends to adopt an ambivalent attitude to the concept of power. The concept is fundamental in sociology but secondary or even disregarded in CA. A closer look at research and the conceptual foundations of CA however demonstrate significant contributions to theories of power. In this paper we aim to demonstrate and discuss these contributions, however, also arguing for an expansion of the CA approach in dialogue with sociological theories to engage in the sociological analysis of power as an essential feature of social relationships and social organization. Based on a general definition of power, as the transformative capacities of social agents in virtue of their social relationships, we discuss how power is interactionally achieved and negotiated, but also conditioned by social institutions and structures that extend beyond the contexts of situated encounters. The paper is divided into two main sections. The first section presents central contributions of CA in relation to the distinctions between power over and power to, authority as a legitimate form of power, and deontics as a key concept in the analysis of power. The second section critically considers the tendency in CA to localize power solely to actions in interaction, and to conflate structure and action, which constraints the analysis and explanations of power. We present examples of how analyses of power, grounded in CA, can be extended to account for the dynamics of social structures and realities beyond the interactional encounters.