Business decision-makers struggle to grasp the full extent of their actions and responsibilities regarding the benefits and externalities of digital technologies. A growing discussion on corporate digital responsibility (CDR) emerged, addressing the raised concerns and identifying opportunities. However, some developments indicate that discussions on principles barely find their way into organizational practice, likely lacking implementation into corporate governance. Our research synthesizes contributions from CDR literature on the corporate governance mission, measures, and frameworks to determine the status quo. The assessed research map on digital responsibility in corporate governance exhibits nine principles-to-practice gaps. As a first narrowing of the gaps, we then turn to the related research field of corporate (social) responsibility (C(S)R) to examine whether the research encompasses learnings to narrow the gaps. In a synthesized coherence twelve C(S)R learnings are determined providing general learnings on corporate responsibility dynamics, established content findings, and insights on proven research models.