Hydrogen embrittlement (HE) refers to the degraded mechanical properties of high-strength steels due to the hydrogen effect, such as tensile strength, elongation as well as area reduction. HE can initiate a fracture due to residual stress or in service, leading to catastrophic failures in critical infrastructure. While hydrogen embrittlement has been studied for many years, a fundamental understanding of hydrogen embrittlement (HE) mechanisms remains incomplete. Typical mechanisms like hydrogen-enhanced decohesion (HEDE) and hydrogen-enhanced localized plasticity (HELP), remain poorly quantified experimentally, and there is a lack of numerical simulations on this topic. Though numerous theoretical models have been proposed, critical gaps persist in experimental validation data. How to choose proper models is still a confusing key question with an unclear mechanistic understanding of HE. This review systematically evaluates the role of the Finite Element Method in modeling HE mechanisms and predicting material-specific failures. It discusses cohesive zone modelling (CZM) as an application of numerical models to hydrogen embrittlement. This model studies different mechanisms, such as HEDE and HELP. Effective numerical models can highlight the necessity for enhanced integration between experimental characterization and computational validation and efficiently predict HE failure.