A intelligent reflecting surface (IRS) can intelligently configure wavefronts such as amplitude, frequency, phase, and even polarization through passive reflections and without requiring any radio frequency (RF) chains. It is predicted to be a revolutionizing technology with the capability to alter wireless communication to enhance both spectrum and energy efficiencies with low expenditure and low energy consumption. Similarly, unmanned aerial vehicle (UAV) communication has attained a significant interest by research fraternity due to high mobility, flexible deployment, and easy integration with other technologies. However, UAV communication can face obstructions and eavesdropping in real-time scenarios. Recently, it is envisaged that IRS and UAV can combine together to achieve unparalleled opportunities in difficult environments. Both technologies can achieve enhanced performance by proactively altering the wireless propagation through maneuver control and smart signal reflections in three-dimensional space. This study briefly discusses IRS-assisted UAV communications. We survey the existing literature on this emerging research topic for both ground and airborne scenarios. We highlight several emerging technologies and application scenarios for future wireless networks. This study goes one step further to elaborate research opportunities to design and optimize wireless systems with low energy footprint and at low cost. Finally, we shed some light on open challenges and future research directions for IRS-assisted UAV communication.