Despite the power constraints, UAVs (Unmanned aerial vehicles) have an inherent advantage of lower air traffic, making them an attractive alternative to high-speed transportation and logistics. Many algorithmic models are used for empirical analysis based on network architecture, data forwarding, and comprehensive performance variation regarding routing delay, energy efficiency, throughput, network overheads, scalability, bandwidth, link failure probability, etc. Due to such a wide variation in protocol availability, and respective performance measures, it is difficult for researchers and network designers to select the best possible models suited for their network application. Moreover, this wide variation increases network design time and cost-to-market, which affects UAV network viability. Thus, there is a need to simplify this process of routing model selection. This motivates us to frame this survey article. A comprehensive survey of recently proposed UAV routing models is proposed. This survey includes a description of reviewed models and their nuances, advantages, limitations, and future research possibilities. Upon referring to this survey, readers could contemplate the characteristics of respective models and identify improvement areas in each. Based on observation, researchers can select the best-suited routing models of UAVs for their applications. This review is accompanied by an in-depth statistical analysis of these models and their comparison concerning computational complexity, throughput, energy efficiency, end-to-end delay, and routing efficiency. It will assist researchers and UAV network designers in selecting the most optimum context-specific models for their network deployments, thereby lowering network design time and cost of deployment.