Abstract. Deep Learning techniques have been increasingly used in flood risk management to overcome the limitations of accurate, yet slow, numerical models, and to improve the results of traditional methods for flood mapping. In this paper, we review 45 recent publications to outline the state-of-the-art of the field, identify knowledge gaps, and propose future research directions. The review focuses on the type of deep learning models used for various flood mapping applications, the flood types considered, the spatial scale of the studied events, and the data used for model development. The results show that models based on convolutional layers are usually more accurate as they leverage inductive biases to better process the spatial characteristics of the flooding events. Traditional models based on fully-connected layers, instead, provide accurate results when coupled with other statistical models. Deep learning models showed increased accuracy when compared to traditional approaches and increased speed when compared to numerical methods. While there exist several applications in flood susceptibility, inundation, and hazard mapping, more work is needed to understand how deep learning can assist real-time flood warning during an emergency, and how it can be employed to estimate flood risk. A major challenge lies in developing deep learning models that can generalize to unseen case studies and sites. Furthermore, all reviewed models and their outputs, are deterministic, with limited considerations for uncertainties in outcomes and probabilistic predictions. The authors argue that these identified gaps can be addressed by exploiting recent fundamental advancements in deep learning or by taking inspiration from developments in other applied areas. Models based on graph neural networks and neural operators can work with arbitrarily structured data and thus should be capable of generalizing across different case studies and could account for complex interactions with the natural and built environment. Neural operators can also speed up numerical models while preserving the underlying physical equations and could thus be used for reliable real-time warning. Similarly, probabilistic models can be built by resorting to Deep Gaussian Processes.