Whole‐genome approaches, which are replacing targeted tests in research and clinical practice, increase the chances of ‘incidental findings’ (IFs) – that is, those unrelated to the reason for the test. IFs raise several challenging questions, such as are researchers obliged to disclose IFs, and does this change if the researcher is also a clinician? How can the clinical significance of IFs be determined, and what significance level should determine disclosure? Could family members be tested to help to clarify significance, and if so, how? What should happen if adult‐onset risks are found in children or prenatally? No consensus currently exists about disclosing IFs from research, or about how participants can be helped to make decisions about and give consent (not) to receive them. We recommend that as more research studies that use genome‐wide tests are launched, longitudinal empirical work be conducted to explore participants' experiences and inform best practice for consent and, where relevant, feedback.