Understanding the climatic conditions that drive vector-borne disease emergence and spread is critically important for understanding current infectious disease dynamics and predicting how they may shift with climate change. Temperature, rainfall, and humidity can influence vector abundance, distribution, and vectorial capacity (the number of infectious vector bites per person) by affecting a variety of vector traits, including survival, reproduction, and development. Using dengue and chikungunya as examples, I will discuss how climate factors impact the abundance of the Aedes aegypti mosquito vector and disease transmission. Often temperature, rainfall, and humidity influence mosquito traits differently across their environmental ranges. For instance, the relationships between temperature and multiple mosquito traits are unimodal, which has led to the prediction of an intermediate optimal temperature for disease transmission, which is lower than previously expected. We are incorporating these climate-driven traits into mathematical models to better understand how climate affects dengue and chikungunya transmission in Africa and South America, using field entomology and epidemiology data from Kenya and Ecuador. These models can help us predict disease transmission in the near future and understand how global climate change is likely to shift transmission in space and time in the longer term. Further, these results have implications for understanding where other Aedes aegypti-vectored diseases could circulate, including currently known diseases of concern such as Zika and yellow fever, as well as emerging pathogens such as Mayaro virus.