BACKGROUND: Timely, accurate, and comprehensive estimates of SARS-CoV-2 daily infection rates, cumulative infections, the proportion of the population that has been infected at least once, and the effective reproductive number (Reffective) are essential for understanding the determinants of past infection, current transmission patterns, and a population's susceptibility to future infection with the same variant. Although several studies have estimated cumulative SARS-CoV-2 infections in select locations at specific points in time, all of these analyses have relied on biased data inputs that were not adequately corrected for. In this study, we aimed to provide a novel approach to estimating past SARS-CoV-2 daily infections, cumulative infections, and the proportion of the population infected, for 190 countries and territories from the start of the pandemic to Nov 14, 2021. This approach combines data from reported cases, reported deaths, excess deaths attributable to COVID-19, hospitalisations, and seroprevalence surveys to produce more robust estimates that minimise constituent biases. METHODS: We produced a comprehensive set of global and location-specific estimates of daily and cumulative SARS-CoV-2 infections through Nov 14, 2021, using data largely from Johns Hopkins University (Baltimore, MD, USA) and national databases for reported cases, hospital admissions, and reported deaths, as well as seroprevalence surveys identified through previous reviews, SeroTracker, and governmental organisations. We corrected these data for known biases such as lags in reporting, accounted for under-reporting of deaths by use of a statistical model of the proportion of excess mortality attributable to SARS-CoV-2, and adjusted seroprevalence surveys for waning antibody sensitivity, vaccinations, and reinfection from SARS-CoV-2 escape variants. We then created an empirical database of infection-detection ratios (IDRs), infection-hospitalisation ratios (IHRs), and infection-fatality ratios (IFRs). To estimate a complete time series for each location, we developed statistical models to predict the IDR, IHR, and IFR by location and day, testing a set of predictors justified through published systematic reviews. Next, we combined three series of estimates of daily infections (cases divided by IDR, hospitalisations divided by IHR, and deaths divided by IFR), into a more robust estimate of daily infections. We then used daily infections to estimate cumulative infections and the cumulative proportion of the population with one or more infections, and we then calculated posterior estimates of cumulative IDR, IHR, and IFR using cumulative infections and the corrected data on reported cases, hospitalisations, and deaths. Finally, we converted daily infections into a historical time series of Reffective by location and day based on assumptions of duration from infection to infectiousness and time an individual spent being infectious. For each of these quantities, we estimated a distribution based on an ensemble framework that captured uncertainty in data sources, model design, and parameter assumptions. FINDINGS: Global daily SARS-CoV-2 infections fluctuated between 3 million and 17 million new infections per day between April, 2020, and October, 2021, peaking in mid-April, 2021, primarily as a result of surges in India. Between the start of the pandemic and Nov 14, 2021, there were an estimated 3·80 billion (95% uncertainty interval 3·44-4·08) total SARS-CoV-2 infections and reinfections combined, and an estimated 3·39 billion (3·08-3·63) individuals, or 43·9% (39·9-46·9) of the global population, had been infected one or more times. 1·34 billion (1·20-1·49) of these infections occurred in south Asia, the highest among the seven super-regions, although the sub-Saharan Africa super-region had the highest infection rate (79·3 per 100 population [69·0-86·4]). The high-income super-region had the fewest infections (239 million [226-252]), and southeast Asia, east Asia, and Oceania had the lowest infection rate (13·0 per 100 population [8·4-17·7]). The cumulative proportion of the population ever infected varied greatly between countries and territories, with rates higher than 70% in 40 countries and lower than 20% in 39 countries. There was no discernible relationship between Reffective and total immunity, and even at total immunity levels of 80%, we observed no indication of an abrupt drop in Reffective, indicating that there is not a clear herd immunity threshold observed in the data. INTERPRETATION: COVID-19 has already had a staggering impact on the world up to the beginning of the omicron (B.1.1.529) wave, with over 40% of the global population infected at least once by Nov 14, 2021. The vast differences in cumulative proportion of the population infected across locations could help policy makers identify the transmission-prevention strategies that have been most effective, as well as the populations at greatest risk for future infection. This information might also be useful for targeted transmission-prevention interventions, including vaccine prioritisation. Our statistical approach to estimating SARS-CoV-2 infection allows estimates to be updated and disseminated rapidly on the basis of newly available data, which has and will be crucially important for timely COVID-19 research, science, and policy responses. FUNDING: Bill & Melinda Gates Foundation, J Stanton, T Gillespie, and J and E Nordstrom.