Arthropod-borne viruses (arboviruses) circulate in nature between arthropod vectors and vertebrate hosts. Arboviruses often cause devastating diseases in vertebrate hosts, but they typically do not cause significant pathology in their arthropod vectors. Following oral acquisition of a viremic bloodmeal from a vertebrate host, the arbovirus disease cycle requires replication in the cellular environment of the arthropod vector. Once the vector has become systemically and persistently infected, the vector is able to transmit the virus to an uninfected vertebrate host. In order to systemically infect the vector, the virus must cope with innate immune responses and overcome several tissue barriers associated with the midgut and the salivary glands. In this review we describe, in detail, the typical arbovirus infection route in competent mosquito vectors. Based on what is known from the literature, we explain the nature of the tissue barriers that arboviruses are confronted with in a mosquito vector and how arboviruses might surmount these barriers. We also point out controversial findings to highlight particular areas that are not well understood and require further research efforts.