Recently, owing to the high mobility and low cost of drones, drone-based delivery systems have shown considerable potential for ensuring flexible and reliable parcel delivery. Several crucial design issues must be considered to design such systems, including route planning, payload weight consideration, distance measurement, and customer location. In this paper, we present a survey of emerging drone routing algorithms for drone-based delivery systems, emphasizing three major drone routing aspects: trajectory planning, charging, and security. We focus on practical design considerations to ensure efficient, flexible, and reliable parcel delivery. We first discuss the potential issues arising when designing such systems. Next, we present a novel taxonomy based on the above-mentioned three aspects. We extensively review each algorithm for drone routing in terms of key features and operational characteristics. Furthermore, we compare the algorithms in terms of their main idea, advantages, limitations, and performance aspects. Finally, we present open research challenges to motivate further research in this field. In particular, we focus on the major aspects that researchers and engineers need to consider in order to design effective and reliable drone routing algorithms for drone-based delivery systems.