Intelligent reflecting surface (IRS) can smartly adjust the wavefronts in terms of phase, frequency, amplitude and polarization via passive reflections and without any need of radio frequency (RF) chains. It is envisaged as an emerging technology which can change wireless communication to improve both energy and spectrum efficiencies with low energy consumption and low cost. It can intelligently configure the wireless channels through a massive number of cost effective passive reflecting elements to improve the system performance. Similarly, unmanned aerial vehicle (UAV) communication has gained a viable attention due to flexible deployment, high mobility and ease of integration with several technologies. However, UAV communication is prone to security issues and obstructions in real-time applications. Recently, it is foreseen that UAV and IRS both can integrate together to attain unparalleled capabilities in difficult scenarios. Both technologies can ensure improved performance through proactively altering the wireless propagation using smart signal reflections and maneuver control in three dimensional (3D) space. IRS can be integrated in both aerial and terrene environments to reap the benefits of smart reflections. This study briefly discusses UAV communication, IRS and focuses on IRS-assisted UAC communications. It surveys the existing literature on this emerging research topic and highlights several promising technologies which can be implemented in IRS-assisted UAV communication. This study also presents several application scenarios and open research challenges. 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 future research aspects for IRS-assisted UAV communication.