Despite dominant technology discourses focusing on novelty, growth, speed and effectiveness, the sociologically informed analyses of datafication have, to some extent implicitly, emphasised brokenness and glitches as productive and inherent elements of a datafied society. This article asks: “How can sociologically informed analyses of datafication be expanded to further guide and understand datafied societies?” The goal of this article is twofold: first, I depart from the idea of “broken world thinking” and the notion of glitch, and discuss some examples of previous research where sociologically informed and critical analyses of datafication provide a unique perspective of looking “beyond the glitch” and deeper into power relations and social structures. Second, I discuss some areas and directions for further exploration, suggesting that looking beyond the glitch is not only a productive perspective but that it also reminds us to keep up with the critical sociological imagination.