Healthcare is amongst the most complex of human systems. Coordinating activities and integrating newer with older ways of treating patients while delivering high-quality, safe care, is challenging. Three landmark reports in 2018 led by (1) the Lancet Global Health Commission, (2) a coalition of the World Health Organization, the Organisation for Economic Co-operation and Development and the World Bank, and (3) the National Academies of Sciences, Engineering and Medicine of the United States propose that health systems need to tackle care quality, create less harm and provide universal health coverage in all nations, but especially low- and middle-income countries. The objective of this study is to review these reports with the aim of advancing the discussion beyond a conceptual diagnosis of quality gaps into identification of practical opportunities for transforming health systems by 2030. We analysed the reports via text-mining techniques and content analyses to derive their key themes and concepts. Initiatives to make progress include better measurement, using the capacities of information and communications technologies, taking a systems view of change, supporting systems to be constantly improving, creating learning health systems and undergirding progress with effective research and evaluation. Our analysis suggests that the world needs to move from 2018, the year of reports, to the 2020s, the decade of action. We propose three initiatives to support this move: first, developing a blueprint for change, modifiable to each country's circumstances, to give effect to the reports' recommendations; second, to make tangible steps to reduce inequities within and across health systems, including redistributing resources to areas of greatest need; and third, learning from what goes right to complement current efforts focused on reducing things going wrong. We provide examples of targeted funding which would have major benefits, reduce inequalities, promote universality and be better at learning from successes as well as failures. The reports contain many recommendations, but lack an integrated, implementable, 10-year action plan for the next decade to give effect to their aims to improve care to the most vulnerable, save lives by providing high-quality healthcare and shift to measuring and ensuring better systems- and patient-level outcomes. This article signals what needs to be done to achieve these aims.