Background Cervical screening and human papillomavirus (HPV) vaccination have been implemented in most high-income countries; however, coverage is low in low-income and middle-income countries (LMICs). In 2018, the Director-General of WHO announced a call to action for the elimination of cervical cancer as a public health problem. WHO has called for global action to scale-up vaccination, screening, and treatment of precancer, early detection and prompt treatment of early invasive cancers, and palliative care. An elimination threshold in terms of cervical cancer incidence has not yet been defined, but an absolute rate of cervical cancer incidence could be chosen for such a threshold. In this study, we aimed to quantify the potential cumulative effect of scaled up global vaccination and screening coverage on the number of cervical cancer cases averted over the 50 years from 2020 to 2069, and to predict outcomes beyond 2070 to identify the earliest years by which cervical cancer rates could drop below two absolute levels that could be considered as possible elimination thresholds—the rare cancer threshold (six new cases per 100 000 women per year, which has been observed in only a few countries), and a lower threshold of four new cases per 100 000 women per year. Methods In this statistical trends analysis and modelling study, we did a statistical analysis of existing trends in cervical cancer worldwide using high-quality cancer registry data included in the Cancer Incidence in Five Continents series published by the International Agency for Research on Cancer. We then used a comprehensive and extensively validated simulation platform, Policy1-Cervix, to do a dynamic multicohort modelled analysis of the impact of potential scale-up scenarios for cervical cancer prevention, in order to predict the future incidence rates and burden of cervical cancer. Data are presented globally, by Human Development Index (HDI) category, and at the individual country level. Findings In the absence of further intervention, there would be 44·4 million cervical cancer cases diagnosed globally over the period 2020–69, with almost two-thirds of cases occurring in low-HDI or medium-HDI countries. Rapid vaccination scale-up to 80–100% coverage globally by 2020 with a broad-spectrum HPV vaccine could avert 6·7–7·7 million cases in this period, but more than half of these cases will be averted after 2060. Implementation of HPV-based screening twice per lifetime at age 35 years and 45 years in all LMICs with 70% coverage globally will bring forward the effects of prevention and avert a total of 12·5–13·4 million cases in the next 50 years. Rapid scale-up of combined high-coverage screening and vaccination from 2020 onwards would result in average annual cervical cancer incidence declining to less than six new cases per 100 000 individuals by 2045–49 for very-high-HDI countries, 2055–59 for high-HDI countries, 2065–69 for medium-HDI countries, and 2085–89 for low-HDI countries, and to less than four cases per 100 000 by 2055–59 for very-high-HDI countries, 2065–69 for high-HDI countries, 2070–79 for medium-HDI countries, and 2090–2100 or beyond for low-HDI countries. However, rates of less than four new cases per 100 000 would not be achieved in all individual low-HDI countries by the end of the century. If delivery of vaccination and screening is more gradually scaled up over the period 2020–50 (eg, 20–45% vaccination coverage and 25–70% once-per-lifetime screening coverage by 2030, increasing to 40–90% vaccination coverage and 90% once-per-lifetime screening coverage by 2050, when considered as average coverage rates across HDI categories), end of the century incidence rates will be reduced by a lesser amount. In this scenario, average cervical cancer incidence rates will decline to 0·8 cases per 100 000 for very-high-HDI countries, 1·3 per 100 000 for high-HDI countries, 4·4 per 100 000 for medium-HDI countries, and 14 per 100 000 for low-HDI countries, by the end of the century. Interpretation More than 44 million women will be diagnosed with cervical cancer in the next 50 years if primary and secondary prevention programmes are not implemented in LMICs. If high coverage vaccination can be implemented quickly, a substantial effect on the burden of disease will be seen after three to four decades, but nearer-term impact will require delivery of cervical screening to older cohorts who will not benefit from HPV vaccination. Widespread coverage of both HPV vaccination and cervical screening from 2020 onwards has the potential to avert up to 12·5–13·4 million cervical cancer cases by 2069, and could achieve average cervical cancer incidence of around four per 100 000 women per year or less, for all country HDI categories, by the end of the century. A draft global strategy to accelerate cervical cancer elimination, with goals and targets for the period 2020–30, will be considered at the World Health Assembly in 2020. The findings presented here have helped inform initial discussions of elimination targets, and ongoing comparative modelling with other groups is supporting the development of the final goals and targets for cervical cancer elimination. Funding National Health and Medical Research Council (NHMRC) Australia, part-funded via the NHMRC Centre of Excellence for Cervical Cancer Control (C4; APP1135172).