Floods are one of the most destructive and frequent natural hazards, and recent advances in artificial intelligence (AI) offer new opportunities to improve prediction, real-time monitoring, and flood mapping. In this review, we survey and analyze current AI based approaches used in flood management, including convolutional neural networks (CNNs), deep neural networks (DNNs), recurrent models such as LSTM and RNN, physics-informed architectures, multimodal systems, and IoT-integrated frameworks. These models utilize diverse data sources such as satellite imagery, UAV observations, social media, hydrological sensors, and remote sensing products to enhance forecasting accuracy and situational awareness. Additionally, we examine non-deep learning machine-learning methods such as Random Forests, XGBoost, and regression-based models that are still effective in data-scarce environments. By comparing these techniques across prediction, real-time assessment, and mapping applications, we aim to highlight their strengths, limitations, and operational potential. This review seeks to provide researchers, practitioners, and policymakers with a consolidated understanding of the current landscape of AI flood modeling and to introduce future development of reliable flood risk management systems.