Background Several open science-promoting initiatives have been proposed to improve the quality of biomedical research, including initiatives for assessing researchers’ open science behaviour as criteria for promotion or tenure. Yet there is limited evidence to judge whether the interventions are effective. This review aimed to summarise the literature, identifying open science practices related to researcher assessment, and map the extent of evidence of existing interventions implemented to assess researchers and research impact. Methods A scoping review using the Joanna Briggs Institute Scoping Review Methodology was conducted. We included all study types that described any open science practice-promoting initiatives proposed or implemented to assess researchers and research impact, in health sciences, biomedicine, psychology, and economics. Data synthesis was quantitative and descriptive. Results Among 18,020 identified documents, 27 articles were selectedfor analysis. Most of the publications were in the field of health sciences (n = 10), and were indicated as research culture, perspective, commentary, essay, proceedings of a workshop, research article, world view, opinion, research note, editorial, report, and research policy articles (n = 22). The majority of studies proposed recommendations to address problems regarding threats to research rigour and reproducibility that were multi-modal (n = 20), targeting several open science practices. Some of the studies based their proposed recommendations on further evaluation or extension of previous initiatives. Most of the articles (n = 20) did not discuss implementation of their proposed intervention. Of the 27 included articles, 10 were cited in policy documents, with The Leiden Manifesto being the most cited (104 citations). Conclusion This review provides an overview of proposals to integrate open science into researcher assessment. The more promising ones need evaluation and, where appropriate, implementation. Study registration https://osf.io/ty9m7