Debris flows are among the most catastrophic natural phenomena, attracting the interest of researchers, engineers and government agencies. The complexity of the physical process has led to the development of numerous mathematical models to simulate and deeper understand the propagation of debris flows. Nevertheless, the intrinsic characteristics of models are not all suitable for every process observed in nature. Hence, this review identifies the main features of the different modelling approaches for debris flows and proposes recommendations for a more rigorous selection of models. The classification of the models is based on the following features: (1) phases of the flow; (2) entrainment of materials into the flow; (3) constitutive relationships; (4) spatial dimensionality; and (5) the solution methods. We discuss the advantages and limitations of the most remarkable contributions by comparing the available mathematical models for debris flows based on each feature. A selection strategy is proposed to be supported by the main assumptions of the models, the classification features and some dimensionless numbers evoked in debris flow research. As a result of this review, the principal considerations can be summarised as follows. First, the complexity of the models has been increasing with the enhanced understanding of debris flows and advances in technology. Thus, the multiphase approach, more sophisticated constitutive relationships, three-dimensional representations and numerical methods requiring higher computational cost are becoming noteworthy. Secondly, three-dimensional representations are better suited for the study of specific and small-scale debris-flow processes, while the two-dimensional depth-averaged approach is still the most appropriate for field applications. Finally, the most recognised and recent models are highlighted and concisely compiled in a table to provide an overview of the options.

泥石流是最具灾难性的自然现象之一，吸引了研究人员、工程师和政府机构的兴趣。物理过程的复杂性导致开发了许多数学模型来模拟和更深入地了解泥石流的传播。然而，模型的内在特征并不都适用于自然界中观察到的每个过程。因此，本综述确定了泥石流不同建模方法的主要特征，并就更严格的模型选择提出了建议。模型的分类基于以下特征：（1）流动的阶段；(2) 物料夹带入流中；（三）构成关系；(4) 空间维度；(5)解决方法。我们通过比较基于每个特征的泥石流的可用数学模型来讨论最显着贡献的优点和局限性。提出了一种选择策略，以支持模型的主要假设、分类特征和泥石流研究中引起的一些无量纲数。作为本次审查的结果，主要考虑因素可总结如下。首先，随着对泥石流理解的加深和技术的进步，模型的复杂性不断增加。因此，需要更高计算成本的多相方法、更复杂的本构关系、三维表示和数值方法正变得值得注意。第二，三维表示更适合研究特定的小规模泥石流过程，而二维深度平均方法仍然最适合现场应用。最后，最受认可和最近的模型被突出显示并简明扼要地汇总在一个表格中，以提供选项的概述。