Social media data are increasingly used to study a variety of social phenomena. This development is based on the assumption that digital traces left on social media can provide insights into the nature of human interaction. In this research, we turn our attention to what remains invisible in research based on social media data. Using Andrea Brighenti’s work on ‘social visibility’ as a point of departure, we unpack data invisibilities, as they are created within four dimensions: people and intentionality, technologies and tools, accessibility and form, and meaning and imaginaries. We introduce the notion of quasi-visible data as an intermediary between visible and invisible data highlighting the processual character of data invisibilities. With this conceptual framework we contribute to developing a more reflective and ethical field of research into the study of social phenomena based on social media data. We conclude by arguing that distancing ourselves from the assumption that all social media data are visible and focusing on the invisible will enhance our understanding of digital data.