Rapid restoration of communication infrastructure is essential for effective coordination, emergency response, and resource allocation in post-disaster scenarios. As conventional communication systems are often damaged or rendered inaccessible during disasters, Unmanned Aerial Vehicles (UAVs) have emerged as a promising alternative for establishing temporary, ad-hoc communication networks. However, despite growing academic and practical interest, UAV-based communication recovery remains in its early stages, facing numerous technical and operational challenges that hinder widespread and effective adoption in complex disaster environments. In response, this study conducts a systematic literature review following the PRISMA protocol to synthesize the current state of knowledge on UAVs applications for Aerial Base Stations (ABSs) deployed as temporary replacements for disaster-affected terrestrial base stations. The review identified key concepts and system architectures, hardware configurations, deployment strategies, emerging AI-driven autonomy, and energy optimization approaches. The findings reveal notable technological progress in energy harvesting (e.g., solar-assisted and tethered platforms) and AI-driven energy conservation strategies; however, persistent limitations, particularly sustained endurance and unresolved coverage–capacity trade-offs, continue to hinder real-world implementation due to the lack of robust real-world validation. By consolidating these insights, the study provides a comprehensive assessment of current advancements and identifies strategic priorities for future research and policy development. This plays a crucial role in supporting the design and deployment of resilient, adaptive, and efficient UAV-based ABSs systems in disaster management contexts.