Granular materials are abundant in nature, and in most industries, either the initial constituents or final products are in granular form during a production or processing stage. Industrial processes and equipment for the handling of bulk solids can only be improved if we can understand, model and predict the material behaviour. The discrete element method (DEM) is a numerical tool well-suited for this purpose and has been used by researchers and engineers to analyse various industrial applications and processes. However, before any bulk scale modelling can be undertaken, the input parameters must be carefully calibrated to obtain accurate results. The calibration of parameter values for non-cohesive materials has reached a level of maturity; however, the calibration of cohesive materials requires more research. This paper details the most prevalent contact models used to model cohesive materials—presented in a consistent notation. Moreover, the significant differences between the models are highlighted to provide a reference for engineers and researchers to select the most appropriate model for a specific application. Finally, a critical review of calibration experiments and methodologies often used for cohesive materials is also presented. This provides a solid basis for DEM practitioners to select the most appropriate calibration methodology for their application and for researchers to extend the current state-of-the-art practices.