The representation of traditionally scientifically underserved groups in genomic research continues to be low despite concerns about equity and social justice and the scientific and clinical need. Among the factors that account for this are a lack of trust in the research community and limited diversity in this community. The success of the multiple initiatives that aim to improve representation relies on the willingness of underrepresented populations to make data and samples available for research and clinical use. In this narrative review, we propose that this requires building trust, and set out four approaches to demonstrating trustworthiness, including increasing diversity in the research workforce, and meaningful engagement with underrepresented communities in a culturally and linguistically appropriate manner. Capacity building globally will ensure that actual and perceived exploitation and 'helicopter' research could be eliminated. [Abstract copyright: Copyright © 2022 The Authors. Published by Elsevier B.V. All rights reserved.]