Flooding stands as one of the world’s most devastating natural hazards, accounting for lost lives, economic damage, and ecosystem degradation. Over the past five decades, flood inundation models have emerged as essential tools for flood forecasting and risk management. Through an analysis of publications from 1970 to 2023, this review provides a foundational understanding of state-of-the-science flood model developments. The evolution of flood models in recent decades has been marked by significant technological advances, including enhancing traditional numerical modeling approaches and deploying them with widespread use of large-scale simulation and satellite remote sensing. The field has matured substantially over the past 50 years, and it seems to have reached an inflection point at which major research is poised to progress. The most ambitious research directions are those that involve coupling flood models with models in diverse fields and involve: (1) atmospheric sciences to construct a two-way coupled flood-land surface-atmosphere model, (2) epidemiology to assess the health impacts of floods, (3) economics to help develop a flood model damage footprint framework to quantify financial harm to those who occupy urban and agricultural land, (4) ecology to evaluate and quantify flood-induced ecological damage, (5) further development of groundwater flooding, glacial lake outburst flooding, sedimentation-induced flooding, plus investigation of the joint impact of multiple compounding flood types, (6) responsible advancement of AI-based flood models, (7) greater assimilation of multiple data sources that include high resolution satellite and drone imagery, crowdsourcing, and video data. Building on the broad foundation of flood-modeling research conducted over many decades, these eight avenues offer promising opportunities to further address the combined challenges of escalating climate, land-use, and demographic changes.