The United Kingdom Research and Innovation (UKRI) in collaboration with the UK Forum for Responsible Research Metrics and the National Research Foundation (NRF) in South Africa delivered a Global Research Council Virtual Conference on Responsible Research Assessment (RRA) in November 2020. International speakers presented existing practices and approaches to responsible research assessment (RRA). Funders discussed their current engagement on issues of RRA and how to improve assessment approaches to support a diverse research culture. This report presents the context for the conference, some key analytics and the main discussion outcomes in five themes. It also proposes next steps for the Global Research Council (GRC). In addition, sessions from the 2020 GRC Virtual Conference on Responsible Research Assessment can be viewed on the GRC YouTube channel.