A myriad of factors favor the emergence and re-emergence of arthropod-borne viruses (arboviruses), including migration, climate change, intensified livestock production, an increasing volume of international trade and transportation, and changes to ecosystems (e.g., deforestation and loss of biodiversity). Consequently, arboviruses are distributed worldwide and represent over 30% of all emerging infectious diseases identified in the past decade. Although some arboviral infections go undetected or are associated with mild, flu-like symptoms, many are important human and veterinary pathogens causing serious illnesses such as arthritis, gastroenteritis, encephalitis and hemorrhagic fever and devastating economic loss as a consequence of lost productivity and high mortality rates among livestock. One of the most consistent molecular features of emerging arboviruses, in addition to their near exclusive use of RNA genomes, is the inclusion of viral, non-structural proteins that act as interferon antagonists. In this review, we describe these interferon antagonists and common strategies that arboviruses use to counter the host innate immune response. In addition, we discuss the complex interplay between host factors and viral determinants that are associated with virus emergence and re-emergence, and identify potential targets for vaccine and anti-viral therapies.