The digital transformation of the economy and society is fundamentally changing the possible value creation processes of companies. These changes increasingly involve the processing of personal data into information and knowledge that can be used to create individualised user experiences or gain insights from aggregated data. Customer relationships and the interconnectedness of customers are similarly changing as a result of this digital transformation. As customers become more demanding and involved, voluntary activities that go beyond compliance and regulation are becoming increasingly important. At the same time, companies are increasingly recognising the potential of privacy-friendly goods and services. They are using the heterogeneity of their offerings to develop unique selling propositions that focus on fulfilling their digital responsibilities (e.g., Apple, Samsung). In this way, digital responsibility fosters innovation in goods, services and digital markets. The voluntary responsibility of companies in dealing with digital technologies and creating value from data is discussed under the term 'corporate digital responsibility' (CDR). This young field of research has its origins in the study of corporate social responsibility (CSR) and is often discussed in that context. However, with the growing importance of digital responsibility for organisations and the proliferation of related activities, it is increasingly establishing itself as a discipline in its own right. Correspondingly, research on CDR has also seen a sharp increase in the number of publications since 2019. The paper evaluates existing research approaches in a systematic literature review. It highlights definitional approaches, approaches to describing the entrepreneurial motivation for CDR activities and their consequences for corporations, their business relationships and society. Further, the paper identifies research gaps of CDR and provides a basis for further research. This paper shall also serve as a starting point for organisations to establish their own efforts in this area, as well as for the evaluation of existing activities.