Wildfires have emerged as one of the most destructive natural disasters worldwide, causing catastrophic losses. These losses have underscored the urgent need to improve public knowledge and advance existing techniques in wildfire management. Recently, the use of Artificial Intelligence (AI) in wildfires, propelled by the integration of Unmanned Aerial Vehicles (UAVs) and deep learning models, has created an unprecedented momentum to implement and develop more effective wildfire management. Although existing survey papers have explored learning-based approaches in wildfire, drone use in disaster management, and wildfire risk assessment, a comprehensive review emphasizing the application of AI-enabled UAV systems and investigating the role of learning-based methods throughout the overall workflow of multi-stage wildfire management, including pre-fire (e.g., vision-based vegetation fuel measurement), active-fire (e.g., fire growth modeling), and post-fire tasks (e.g., evacuation planning) is notably lacking. This survey synthesizes and integrates state-of-the-science reviews and research at the nexus of wildfire observations and modeling, AI, and UAVs — topics at the forefront of advances in wildfire management, elucidating the role of AI in performing monitoring and actuation tasks from pre-fire, through the active-fire stage, to post-fire management. To this aim, we provide an extensive analysis of the existing remote sensing systems with a particular focus on the UAV advancements, device specifications, and sensor technologies relevant to wildfire management. We also examine the pre-fire and post-fire management approaches, including fuel monitoring, prevention strategies, as well as evacuation planning, damage assessment, and operation strategies. Additionally, we review and summarize a wide range of computer vision techniques in active-fire management, with an emphasis on Machine Learning (ML), Reinforcement Learning (RL), and Deep Learning (DL) algorithms for wildfire classification, segmentation, detection, and monitoring tasks. Ultimately, we underscore the substantial advancement in wildfire modeling through the integration of cutting-edge AI techniques and UAV-based data, providing novel insights and enhanced predictive capabilities to understand dynamic wildfire behavior.