This Background Paper was prepared to frame the discussion in the 1st Consultation on Strengthening Science Systems within the IIASA-ISC Consultative Science Platform “Bouncing Forward Sustainably: Pathways to a post-COVID-19 world”. The paper briefly discusses the response of science and scientists to the COVID-19 crisis, the dissemination of research results and the input of the science community into public policy. While science responded fairly rapidly with appropriate research and the communication of research to the public and to policy makers, there is clear room for improvement. Drawing from the experience of the COVID-19 crisis, three axes of improvement are identified, namely increased agility, enhanced reliability, and a more effective science-policy-society interface. The paper identifies barriers that constrain and inhibit the effectiveness and efficiency of the science system in terms of these three axes. The barriers include misinformation and pseudoscience; the lack of access to data and to mathematical models; the slow pace of peer review; funding challenges both overall and in efficient allocation to critical issues; public trust in, and understanding of, science. Finally, in relation to science for policy, there are issues of transparency, contestation between scientists proffering advice, the need to widen the disciplinary base of science advice and the importance of adopting an interdisciplinary and systemic approach.