In October 2017, the Scientific Committee on Solar-Terrestrial Physics (SCOSTEP) Bureau established a committee for the design of SCOSTEP's Next Scientific Programme (NSP). The NSP committee members and authors of this paper decided from the very beginning of their deliberations that the predictability of the Sun–Earth System from a few hours to centuries is a timely scientific topic, combining the interests of different topical communities in a relevant way. Accordingly, the NSP was christened PRESTO – PREdictability of the variable Solar–Terrestrial cOupling. This paper presents a detailed account of PRESTO; we show the key milestones of the PRESTO roadmap for the next 5 years, review the current state of the art and discuss future studies required for the most effective development of solar–terrestrial physics.