In unmanned aerial vehicle (UAV)-assisted wireless networks, the potential of the high probability of line-of-sight links could be a disadvantage for other nearby wireless networks because of interference caused by a UAV. For this reason, using interference mitigation techniques (IMTs) for UAV-assisted wireless networks is necessary to minimize interference effects. For instance, the mobility of UAVs gives a chance to manage interference better to avoid being a source of interference or being susceptible to interference. After the first-generation mobile network was introduced in the early 1980s, mobile communication systems were developed through several stages of evolution over the following few decades to satisfy rising demand and more stringent specifications. Different IMTs are needed due to these generations' differences. Unlike previous research, this research presents a systematic review of IMTs in the current and future UAV-assisted wireless networks and discusses their challenges. We also review the current research trends of UAV IMTs and their future insights. Our motivation for conducting this research is the need for a systematic review addressing these issues. In this systematic review, we use a more precise classification of the IMTs for UAV-assisted wireless networks. We classify them into four different techniques, namely, adaptive modulation and coding schemes, dynamic antenna pattern adjustment, dynamic transmit power control, and sub-channel scheduling. Moreover, we discuss the IMTs for UAVs using B5G wireless technologies such as intelligent reflecting surfaces, rate-splitting, super modular massive multiple-input multiple-output, Terahertz communications, holographic beamforming, blockchain-based spectrum sharing, and artificial intelligence and machine learning schemes. Furthermore, we identify the challenges of UAV IMTs and their open research directions such as wireless radio frequency spectrum scarcity, lack of networking scalability, beam distortion, resource-constrained management, and new sources of interference. We believe this research will help researchers choose the best technique to mitigate the interference effects in UAV-assisted wireless networks.