Background: The landslides of the flow-type are dangerous and also challenging to study. A wide literature has been investigating the principal mechanisms governing each stage in which these phenomena can be ideally subdivided: failure, post-failure and propagation. However, holistic contributions and general overviews are very rare. In addition, a number of numerical methods have been issued and validated so that new chances exist to efficiently model those threats. The paper focuses on two classes of rainfall-induced landslides of the flow-type, namely debris flows and debris avalanches. The principal numerical methods are reviewed for modelling the landslide initiation and propagation and are later used for analyzing a series of benchmark slopes and real case histories which are successfully simulated. Results: The rainfall from ground surface and water spring from the bedrock are key factors for slope instability. Pore water pressure plays a relevant role also during the propagation stage. The entrainment of further material makes the propagation patterns complex due to lateral spreading and slow-down of the front of flows. It is shown that the used models are capable to provide useful indications even for combined channelized and unchannelized flows. Conclusions: Notwithstanding the complexity of flow-like landslides and the related challenges in modelling, the understanding and forecasting of such natural hazards is achievable with a satisfactory confidence. Among the key factors, rainfall, pore water pressure and bed entrainment deserves a special attention. Further improvements are expectable as the numerical models are becoming more efficient. Thus, more accurate descriptions of local effects will be possible and also additional mechanisms will be eventually analysed.
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