Big data trends in health research challenge the oversight mechanism of the Research Ethics Committees (RECs). The traditional standards of research quality and the mandate of RECs illuminate deficits in facing the computational complexity, methodological novelty, and limited auditability of these approaches. To better understand the challenges facing RECs, we explored the perspectives and attitudes of the members of the seven Swiss Cantonal RECs via semi-structured qualitative interviews. Our interviews reveal limited experience among REC members with the review of big data research, insufficient expertise in data science, and uncertainty about how to mitigate big data research risks. Nonetheless, RECs could strengthen their oversight by training in data science and big data ethics, complementing their role with external experts and ad hoc boards, and introducing precise shared practices.