Advances in numerical methods have provided useful tools for investigating the complex behaviour of landslides, offering significant support for assessing landslide risk, planning, and designing mitigation measures. Among various methods, the Material Point Method (MPM) has grown in popularity, thanks to its ability to simulate large displacements and it has been increasingly applied to simulate real cases. However, there are still some challenges to be addressed. This work aims to review the current state of the art in modelling real landslide case histories with MPM. It discusses the key numerical features, such as constitutive models, soil-water interaction, and triggering mechanisms, that are essential for capturing the evolution of different types of landslides. The aim is to provide insight into the computational aspects of using MPM and offer guidelines for future applications. Limitations and future perspectives are also mentioned to encourage the development of new solutions for existing numerical challenges and to further extend the applicability of the method in this field.