Drones will be a significant part of future mobile communication networks, serving as mobile users or acting as mobile base stations at sky. Although they will provide several solutions related to mobile communication networks and other non-communication services, drones also possess numerous challenges, especially when it comes to their handover management. Unlike terrestrial networks, drones are mobile devices that move in a three-dimension (3D) environment, which further complicates mobility issues. Therefore, this paper provides an overview on the handover management for connected drones in the future mobile networks. The study summarizes how current research efforts approach the issues that characterize drones, with special focus on the handover process. This work also provides a general concept of drone integration in heterogeneous networks and discusses specific solutions for addressing possible problems. This survey further offers a brief discussion and guidance for upcoming research directions related to connected drones in future heterogeneous networks.