This thesis contributes to the debate about media power by advancing a new theoretical perspective. I critique existing theories of media power and argue that media power as it operates in today's complex media environment can be understood as being based on interactions between the culturally and communicatively symbolic components of media communication and the material features and processes of media through which such symbolic communication occurs. I develop and apply an analytical model capable of spanning these two domains and their complex qualities. To develop the model I adopt a neo-materialist ontology based on Deleuze and Guattari's notion of rhizomatic assemblages, Hertog and McLeod's multi-perspectival frame analysis and DeLanda's theory of the assemblage. I argue that this approach can capture both the symbolic and the material dimensions of media that function through networked, complex and emergent interactions. My analytical model is based on four pillars: hybridity, materiality, choreography and coding. I used the model to guide my empirical fieldwork investigation of three case studies: a public demonstration, an animal rights protest aimed at undermining a well-known brand and the high-profile leaks by NSA whistleblower Edward Snowden in 2013. Ethnography, content analysis and interview data were used to assess my model's suitability for making sense of these three cases. Finally, in the conclusion I propose four future themes that this thesis reveals are significant for research on media power: the importance of institutional adaptation, the role of emotion and affect, the significance of computation and the materiality of technology.