During the last two decades, the world has witnessed the emergence and re-emergence of arthropod-borne viruses, better known as arboviruses. The close contact between sylvatic, rural and peri-urban vector species and humans has been mainly determined by the environment-modifying human activity. The resulting interactions have led to multiple dead-end host infections and have allowed sylvatic arboviruses to eventually adapt to new vectors and hosts, contributing to the establishment of urban transmission cycles of some viruses with enormous epidemiologic impact. The metagenomic next-generation sequencing (NGS) approach has allowed obtaining unbiased sequence information of millions of DNA and RNA molecules from clinical and environmental samples. Robust bioinformatics tools have enabled the assembly of individual sequence reads into contigs and scaffolds partially or completely representing the genomes of the microorganisms and viruses being present in biological samples of clinical relevance. In this review, we describe the different ecological scenarios for the emergence of viral diseases, the virus adaptation process required for the establishment of a new transmission cycle and the usefulness of NGS and computational methods for the discovery and routine genomic surveillance of mosquito-borne viruses in their ecosystems.