Digital transformation (DT) is a major challenge for incumbent organisations with an astonishing failure rate. We review digital transformation in established, old, large, and incumbent organisations adopting a Structured and Computational Literature Review (SLR and CLR). We employ a machine learning algorithm (LDA) to inspect the topics discussed in 103 peer-reviewed studies published between 2010 and 2022 in the fields of Information Management, Innovation Management, Operation Management, Strategic Management and General Management. We extract and discuss the top-five key topics emerging from the studies to understand the state-of-the-art literature on DT in established firms. Then, we advance paradox thinking as a lens to study DT in incumbent settings. We contribute to the DT discourse by providing a multidisciplinary review of the current trends on the topic of DT of in-cumbent firms; moreover, we contribute by advancing paradox thinking as a novel lens to study DT in incumbent organisations, further proposing research questions and avenues; finally, we propose managerial insights in line with paradox thinking to create momentum and thrive as DT champions.