With the Kigali Amendment coming into force in 2019, the Montreal Protocol on Substances that Deplete the Ozone Layer has entered a major new phase in which the production and use of hydrofluorocarbons (HFCs) will be controlled in most major economies. This landmark achievement will enhance the Protocol's already-substantial benefits to climate, in addition to its success in protecting the ozone layer. However, recent scientific advances have shown that challenges lie ahead for the Montreal Protocol, due to the newly discovered production of ozone-depleting substances (ODS) thought to be phased-out, rapid growth of ozone-depleting compounds not controlled under the Protocol, and the potential for damaging impacts of ODS degradation products. This proposal tackles the most urgent scientific questions surrounding these challenges by combining state-of-the-art techniques in atmospheric measurements, laboratory experiments and advanced numerical modelling. The latter will include advanced data science and statistical methods to constrain regional and global trends in ozone and ozone-depleting substances and to better characterise uncertainty.