Climate change is a critical driver in the outbreaks of vector-borne infectious diseases worldwide. Arbovirus vectors, namely, mosquitoes, exhibit strong and nonlinear responses to climatic factors, such as temperature driving changes in infectious disease dynamics. In this review, we highlight key climate change factors that can affect arboviruses and their mosquito vectors across multiple biological levels, emphasizing the consequences for the transmission and spread of viruses impacting human hosts. We examine the complex interplay between environmental changes and vector biology, including life history traits, vector competence, and species interactions. We characterize vector ecology across scales critical for our understanding of forecasting the impacts of climate change on mosquito-borne viruses, predicting disease outbreaks and developing effective control measures.