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Model-based control (MBC) techniques have been successfully developed for flight control applications of unmanned aerial vehicles (UAVs) in recent years. However, their heavy reliance on the fidelity of the plant model coupled with high computational complexity make the design and implementation process challenging. To overcome such challenges, attention has been focused on the use of artificial neural networks (ANNs) to study complex systems since they show promise in system identification and controller design, to say the least. This survey aims to provide a literature review on combining MBC techniques with ANNs for UAV flight control, with the goal of laying the foundation for efficient controller designs with performance guarantees. A brief discussion on frequently-used ANNs is presented along with an analysis of their time complexity. Classification/comparison of existing dynamic modeling approaches and control techniques is provided. Challenging research questions and an envisaged control architecture are also posed for future development.