Online disinformation poses a challenge to democratic societies and has become a prominent issue on the research and political agenda. While many analyses focus on patterns of distribution and reach of disinformation, this article contributes to the analysis of strategies to counter disinformation. Employing a governance perspective, it provides a descriptive analysis of the emerging mix of governance responses in the European system of multilevel governance and on the continuum between market and state. Results of the analysis show that the proliferation of disinformation on social media has developed from a socio-technical mix of platform design, algorithms, human factors and political and commercial incentives. Actors and technologies involved provide a starting point for targets of governance within an accountability network. In practice, national governance responses are uneven across the EU, but individual countries pressing for stronger regulation of internet platforms and a weakening of liability protections. In addition, the European Commission has intensified its efforts to combat disinformation and put additional pressure on platforms to take action and provide some level of transparency. However, clarity about the effects of these measures is blurred by contradicting evidence and barriers for research to access platforms and relevant data.