Both unmanned aerial vehicles (UAVs) and intelligent reflecting surfaces (IRS) are gaining traction as transformative technologies for upcoming wireless networks. The IRS-aided UAV communication, which introduces IRSs into UAV communications, has emerged in an effort to improve the system performance while also overcoming UAV communication constraints and issues. The purpose of this paper is to provide a comprehensive overview of IRSassisted UAV communications. First, we provide five examples of how IRSs and UAVs can be combined to achieve unrivaled potential in difficult situations. The technological features of the most recent relevant researches on IRS-aided UAV communications from the perspective of the main performance criteria, i.e., energy efficiency, security, spectral efficiency, etc. Additionally, previous research studies on technology adoption as machine learning algorithms. Lastly, some promising research directions and open challenges for IRS-aided UAV communication are presented.