Karst regions represent 7–12% of the Earth's continental area, and about one quarter of the global population is completely or partially dependent on drinking water from karst aquifers. Climate simulations project a strong increase in temperature and a decrease of precipitation in many karst regions in the world over the next decades. Despite this potentially bleak future, few studies specifically quantify the impact of climate change on karst water resources. This review provides an introduction to karst, its evolution, and its particular hydrological processes. We explore different conceptual models of karst systems and how they can be translated into numerical models of varying complexity and therefore varying data requirements and depths of process representation. We discuss limitations of current karst models and show that at the present state, we face a challenge in terms of data availability and information content of the available data. We conclude by providing new research directions to develop and evaluate better prediction models to address the most challenging problems of karst water resources management, including opportunities for data collection and for karst model applications at so far unprecedented scales. Key Points We elaborate the importance of karst water resourcesWe provide a detailed overview of karst modeling approachWe present new methods and directions for their improvement