To advance the study of digital politics it is urgent to complement data analytics with data hermeneutics to be understood as a methodological approach that focuses on the interpretation of the deep structures of meaning in social media conversations as they develop around various political phenomena, from digital protest movements to online election campaigns. The diffusion of Big Data techniques in recent scholarship on political behavior has led to a quantitative bias in the understanding of online political phenomena and a disregard for issues of content and meaning. To solve this problem it is necessary to adapt the hermeneutic approach to the conditions of social media communication, and shift its object of analysis from texts to datasets. On the one hand, this involves identifying procedures to select samples of social media posts out of datasets, so that they can be analysed in more depth. I describe three sampling strategies - top sampling, random sampling and zoom-in sampling - to attain this goal. On the other hand, “close reading” procedures used in hermeneutic analysis need to be adapted to the different quality of digital objects vis-à-vis traditional texts. This can be achieved by analysing posts not only as data-points in a dataset, but also as interventions in a collective conversation, and as utterances of broader “discourses”. The task of interpretation of social media data also requires an understanding of the political and social contexts in which digital political phenomena unfold, as well as taking into account the subjective viewpoints and motivations of those involved, which can be gained through in-depth interviews, and other qualitative social science methods. Data hermeneutics thus holds promise for a closing of the gap between quantitative and qualitative approaches in the study of digital politics, allowing for a deeper and more holistic understanding of online political phenomena.