This article introduces the multidimensional approach to media ownership and control adopted by the Euromedia Ownership Monitor (EurOMo). This monitor emerged as a response to a call of the EU Commission to set up an instrument to improve transparency in media ownership and control. After considering the context of the EU media policy, the text outlines the theoretical and methodological choices of the monitor, advocating for an approach that addresses the topic in several dimensions defined as ‘ownership structure’, ‘management’, ‘economic control’, ‘relations’, ‘distribution’ and ‘public policy’. In the final part, it engages in a critical reflection both on the project and on the political goal of increasing media ownership transparency. Drawing on this experience, it is possible to affirm that there are good conditions for transparency of the basic media ownership structure in Europe, but all other dimensions need better regulatory frameworks and corresponding adaptions in the monitoring instrument.