Background: Aedes aegypti is the principal vector for several important arbovirus diseases, including dengue, chikungunya, yellow fever, and Zika. While recent empirical research has attempted to identify the current global distribution of the vector, the seasonal, and longer-term dynamics of the mosquito in response to trends in climate, population, and economic development over the twentieth and the twenty-first century remains to be elucidated. Methods: In this study, we use a process-based mathematical model to estimate global vector distribution and abundance. The model is based on the lifecycle of the vector and its dependence on climate, and the model sensitivity to socio-economic development is tested. Model parameters were generally empirically based, and the model was calibrated to global databases and time series of occurrence and abundance records. Climate data on temperature and rainfall were taken from CRU TS3.25 (1901-2015) and five global circulation models (CMIP5; 2006-2099) forced by a high-end (RCP8.5) and a low-end (RCP2.6) emission scenario. Socio-economic data on global GDP and human population density were from ISIMIP (1950-2099). Findings: The change in the potential of global abundance in A. aegypti over the last century up to today is estimated to be an increase of 9.5% globally and a further increase of 20 or 30% by the end of this century under a low compared to a high carbon emission future, respectively. The largest increase has occurred in the last two decades, indicating a tipping point in climate-driven global abundance which will be stabilized at the earliest in the mid-twenty-first century. The realized abundance is estimated to be sensitive to socioeconomic development. Interpretation: Our data indicate that climate change mitigation, i.e., following the Paris Agreement, could considerably help in suppressing risks of increased abundance and emergence of A. aegypti globally in the second half of the twenty-first century.