PurposeDigital transformation (DT) is a major challenge for incumbent organisations, as research on this phenomenon has revealed a high failure rate. Given this consideration, this paper reviews the literature on DT in incumbent organisations to identify the main themes and research directions to be undertaken.Design/methodology/approachThe authors adopt a systematic literature review (SLR) and computational literature review (CLR) employing a machine learning algorithm for topic modelling (LDA) to surface the themes discussed in 103 peer-reviewed studies published between 2010 and 2022 in a multidisciplinary article sample.Findings The authors identify and discuss the five main themes emerging from the studies, offering the state-of-the-art of DT in established firms' literature. The authors find that the most discussed topics revolve around the DT of healthcare, the process of renewal and change, the project management, the changes in value performances and capabilities and the consequences on the products of DT. Accordingly, the authors identify the topics overlooked by literature that future studies could tackle, which concern sustainability and contextualisation of the DT phenomenon.Practical implications The authors further propose managerial insights which equip managers with a revolutionary mindset that is not constraining but, rather, integration-seeking. DT is not only about technology (Tabrizi B et al., 2019). Successful DT initiatives require managerial capabilities that foster a sustainable departure from the current organising logic (Markus, 2004). This study pinpoints and prioritises the role that paradox-informed thinking can have to sustain an effective digital mindset (Eden et al., 2018) that allows for the building of momentum in DT initiatives and facilitates the renewal process. Indeed, managers lagging behind DT could shift from an “either-or” solutions mindset where one pole is preferred over the other (e.g. digital or physical) to embracing a “both-and-with” thinking balancing between poles (e.g. digital and physical) to successfully fuse the digital and the legacy (Lewis and Smith, 2022b; Smith, Lewis and Edmondson, 2022), enact the renewal, and build and maintain momentum for DTs. The outcomes of adopting a paradox mindset in managerial practice are enabling learning and creativity, fostering flexibility and resilience and, finally, unleashing human potential (Lewis and Smith, 2014).Social implicationsThe authors propose insight that will equip managers with a mindset that will allow DT to fail less often than current reported rates, which failure may imply potential organisational collapse, financial bankrupt and social crisis.Originality/value The authors offer a multidisciplinary review of the DT complementing existing reviews due to the focus on the organisational context of established organisations. Moreover, the authors advance paradoxical thinking as a novel lens through which to study DT in incumbent organisations by proposing an array of potential research questions and new avenues for research. Finally, the authors offer insights for managers to help them thrive in DT by adopting a paradoxical mindset.