Next generation wireless networks are expected to be greatly supported by unmanned aerial vehicles, which can act as aerial base stations and constitute a promising solution for the exorbitant rise in user demands. This is possible because of unmanned aerial vehicle characteristics such as mobility, flexibility, increased line-of-sight probability, and their ability to access unreachable locations. Extensive research is now widely performed on the deployment, performance analysis, resource management, trajectory optimization, and channel modeling in such networks. This survey article focuses on the different applications and the related algorithms for realizing aerial base stations by thoroughly reviewing each related research area. In a nutshell, this article provides key applications, challenges, and the technology used for the design and analysis of unmanned aerial vehicles as base stations.