Arboviruses are transmitted between arthropod vectors and vertebrate host. Arboviral infection in mosquitoes is initiated when a mosquito feeds on a viremic host. Following ingestion of a viremic blood meal by mosquitoes, virus enters midgut along with the blood, infects and replicates in midgut epithelial cells, and then escapes to the hemocoel, from where it disseminates to various secondary organs including salivary glands. Subsequently, when mosquito bites another host, a new transmission cycle is initiated. The midgut and salivary glands act as anatomical barriers to virus infection and escape. These complex interactions between the virus and vector dictate the vector competence. Thus, vector competence reflects the success in overcoming different barriers within the vector. Along with these, other intrinsic factors like midgut microbiota and immune responses, extrinsic factors like temperature and humidity, and genetic factors like vector genotype and viral genotype have been discussed in this review. Recent advancement on novel molecular tools to study vector competence is also included. Different modes of arboviral transmission like horizontal, vertical, and venereal and how these play role in sustenance and emergence of arboviruses in nature are also discussed. These factors can be exploited to reduce the susceptibility of vectors for the viruses, so as to control arboviral diseases to certain extent.