Flood inundation mapping (FIM) is essential in disaster risk management, infrastructure planning, and climate adaptation. Traditional hydrodynamic models, such as the Hydrologic Engineering Center’s River Analysis System (HEC-RAS) and LISFLOOD-Floodplain (LISFLOOD-FP), provide physically interpretable flood simulations but are often data- and computation-intensive and difficult to scale across regions. In recent years, machine learning (ML) and deep learning (DL) approaches have emerged as data-driven alternatives that leverage remote sensing observations, digital elevation models (DEMs), and hydro-climatic datasets to enable scalable and near-real-time flood mapping. Our review synthesizes recent advances in ML-based flood inundation mapping, categorizing methods into traditional machine learning techniques (e.g., Random Forest (RF), Support Vector Machines (SVM), Gradient Boosting (GB)), deep learning architectures (e.g., Convolutional Neural Networks (CNNs), U-Net, Long Short-Term Memory networks (LSTM)), and emerging hybrid and physics-informed frameworks. We evaluate model performance across flood extent and flood depth estimation tasks, highlighting strengths, limitations, and common benchmarking practices reported in the literature. The review identifies key challenges related to model interpretability, data bias, transferability, and regulatory acceptance, and highlights recent progress in explainable artificial intelligence (XAI), uncertainty-aware modeling, and physics-informed learning as pathways toward operational adoption. By unifying terminology, performance metrics, and methodological comparisons, this review provides a coherent framework for advancing trustworthy, scalable, and decision-relevant flood inundation mapping under increasing climate-driven flood risk.