The Earth’s water resources, totalling 1.386 billion cubic kilometres, predominantly consist of saltwater in oceans. Groundwater plays a pivotal role, with 99% of usable freshwater supporting 1.5–3 billion people as a drinking water source and 60–70% for irrigation. Climate change, with temperature increases and altered precipitation patterns, directly impacts groundwater systems, affecting recharge, discharge, and temperature. Hydrological models are crucial for assessing climate change effects on groundwater, aiding in management decisions. Advanced hydrological models, incorporating data assimilation and improved process representation, contribute to understanding complex systems. Recent studies employ numerical models to assess climate change impacts on groundwater recharge that could help in the management of groundwater. Groundwater vulnerability assessments vary with the spatial and temporal considerations, as well as assumptions in modelling groundwater susceptibility. This review assesses the vulnerability of groundwater to climate change and stresses the importance of accurate assessments for sustainable water resource management. It highlights challenges in assumptions related to soil and aquifer properties, multiple stressors, adaptive capacity, topography and groundwater contamination processes, gradual sea level rise scenarios, and realistic representations of the region of study. With the advancements in hydrological modelling, including the integration of uncertainty quantification and remote sensing data, artificial intelligence could assist in the efforts to improve models for assessing the impacts of climate change on hydrological modelling.