The operational design and planning of drone-based logistics models is a rapidly growing area of scientific research. In this paper, we present a structured, comprehensive, and scalable framework for classifying drone-based delivery systems and their associated routing problems along with a comprehensive review and synthesis of the extant academic literature in this domain. While our proposed classification defines the boundaries and facilitates the comparison between a wide variety of possible drone-based logistics systems, our comprehensive literature review helps to identify and prioritize research gaps that need to be addressed by future work. Our review shows that the extant research reasonably considers some relevant real-world operational constraints. Although the multi-visit multi-drone Pure-play Drone-based (PD) delivery models are popular, the majority of the Synchronized Multi-modal (SM) delivery models focus on formulating and evaluating single-truck, single-drone models. Moreover, the Resupply Multi-modal (RM) models have not received the due attention for research compared to other drone-based delivery models. Our comprehensive review of use cases of drones for delivery indicates that most of the reviewed models are designed for applications in e-commerce and healthcare/emergency services. Other applications, such as food and mail deliveries are still underrepresented in the academic discussion.