A common motivation for increasing open access to research findings and data is the potential to create economic benefits – but evidence is patchy and diverse. This study systematically reviewed the evidence on what kinds of economic impacts (positive and negative) open science can have, how these comes about, and how benefits could be maximized. Use of open science outputs often leaves no obvious trace, so most evidence of impacts is based on interviews, surveys, inference based on existing costs, and modelling approaches. There is indicative evidence that open access to findings/data can lead to savings in access costs, labour costs and transaction costs. There are examples of open science enabling new products, services, companies, research and collaborations. Modelling studies suggest higher returns to R&D if open access permits greater accessibility and efficiency of use of findings. Barriers include lack of skills capacity in search, interpretation and text mining, and lack of clarity around where benefits accrue. There are also contextual considerations around who benefits most from open science (e.g. sectors, small vs larger companies, types of dataset). Recommendations captured in the review include more research, monitoring and evaluation (including developing metrics), promoting benefits, capacity building and making outputs more audience-friendly.