<p>Regardless of the frequency and magnitude, the consequences of flood hazards are strongly connected to the vulnerability of elements at risk (e.g. buildings, people, and infrastructure). It is, therefore, obvious that an analysis and quantification of vulnerability is required for successful risk reduction. Vulnerability is multidimensional (physical, social, economic, institutional, etc.), however, the primary driver of direct costs and threat to human lives is the physical one. We focus here on the physical vulnerability of buildings subject to dynamic flooding occurring in mountain environments. These processes include debris floods, fluvial sediment transport, and debris flows. Furthermore, we included flash flood hazards if these are related to torrential catchments.</p><p>Physical vulnerability to dynamic flooding in mountain areas is a topic that has been under scientific investigation over the last 20 years. Several methods to assess physical vulnerability of buildings towards flash floods, debris flows and hyper-concentrated flows can be found in the literature. The plethora of methods and approaches may be classified under the following three categories: vulnerability matrices, vulnerability curves and vulnerability indices. We provide a short review of these methods which became available over the last decade and which dominate the scientific debate in mountain hazard risk management, giving an emphasis to vulnerability curves. The approaches presented herein are highlighted through case studies from the mountain areas of Europe and beyond, and challenges in vulnerability assessment including data requirements, need for improved event documentation, uncertainties and challenges related to future climate and socio-economic changes are outlined. Finally, a discussion on progress-driving factors such as new technologies (e.g. mobile apps, drones), citizen science and new innovative assessment methods is provided.</p>