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Traditional techniques for identifying disease genes and disease modules involve high-cost clinical experiments and unpredictable time consumption for analysis. Network-based computational approaches usually focus on the systematic study of molecular networks to predict the associations between diseases and genes. The random walk-based method is a network-based approach that utilises biological networks for analysis. As the random walk models efficiently capture the complex interplay among molecules in diseases, it is extensively applied in biological problem-solving based on networks. Despite their comprehensive employment, the fundamentals of random walk and overall background may not be fully understood, leading to misinterpretation of results. This review aims to cover the fundamental knowledge of random walk models for biological network analysis. This study reviewed diffusion-based random walk methods for disease gene prediction and disease module identification. The random walk-based disease gene prediction methods are categorised into node classification and link prediction tasks. This study details the advantages and limitations of each method. Finally, the potential challenges and research directions for future studies on random walk models are highlighted.