Control of aedine mosquito vectors, either by mosquito population reduction or replacement with refractory mosquitoes, may play an essential role in the fight against arboviral diseases. In this review, we will focus on the development and application of biological approaches, both natural or engineered, to limit mosquito vector competence for arboviruses. The study of mosquito antiviral immunity has led to the identification of a number of host response mechanisms and proteins that are required to control arbovirus replication in mosquitoes, though more factors influencing vector competence are likely to be discovered. We will discuss key aspects of these pathways as targets either for selection of naturally resistant mosquito populations or for mosquito genetic manipulation. Moreover, we will consider the use of endosymbiotic bacteria such as Wolbachia, which in some cases have proven to be remarkably efficient in disrupting arbovirus transmission by mosquitoes, but also the use of naturally occurring insect-specific viruses that may interfere with arboviruses in mosquito vectors. Finally, we will discuss the use of paratransgenesis as well as entomopathogenic fungi, which are also proposed strategies to control vector competence.