This paper reviews numerical methods used to simulate desiccation cracks in clayey soils. It examines five numerical approaches: Finite Element (FEM), Lattice Boltzmann (LBM), Discrete Element (DEM), Cellular Automaton (CAM), and Phase Field (PFM) Methods. The paper presents a simplified description of the methods, including their basic numerical formulations. Several factors such as the multiphase nature of soils, heterogeneity, nonlinearities, coupling, scales of analysis, and computational aspects are discussed. The review highlights the characteristics, strengths, and limitations of each method. FEM shows a good capacity to deal with the thermo-hydromechanical behavior of clays when drying that complement well with the ability of DEM to deal with particle interactions as well as LBM, PFM, and CAM to deal with complex crack patterns. The article concludes by reviewing the integration of multiple numerical methods to enhance the simulation of desiccation cracks in clayey soils and proposing what is the best option to continue improving the study of this problem.