INTRODUCTION: We are witnessing an alarming increase in the burden and range of mosquito-borne arboviral diseases. The transmission dynamics of arboviral diseases is highly sensitive to climate and weather and is further affected by non-climatic factors such as human mobility, urbanization, and disease control. As evidence also suggests, climate-driven changes in species interactions may trigger evolutionary responses in both vectors and pathogens with important consequences for disease transmission patterns. AREAS COVERED: Focusing on dengue and chikungunya, we review the current knowledge and challenges in our understanding of disease risk in a rapidly changing climate. We identify the most critical research gaps that limit the predictive skill of arbovirus risk models and the development of early warning systems, and conclude by highlighting the potentially important research directions to stimulate progress in this field. EXPERT OPINION: Future studies that aim to predict the risk of arboviral diseases need to consider the interactions between climate modes at different timescales, the effects of the many non-climatic drivers, as well as the potential for climate-driven adaptation and evolution in vectors and pathogens. An important outcome of such studies would be an enhanced ability to promulgate early warning information, initiate adequate response, and enhance preparedness capacity.