Karst water resources are valuable freshwater sources for around 10% of the world's population. Nonetheless, anthropogenic impacts and global changes have seriously deteriorated karst water quality and dependent ecosystems. Multiscale karstic heterogeneity—referring to the spatial variations of the karst aquifer's physical and chemical characteristics at varying scales—is the main challenge in describing karst flow and contaminant transport dynamics. Solute transport models are powerful tools to represent and predict the spatiotemporal behaviors of contaminant migration in karst water resources. By enhancing our understanding of the transport processes, the solute transport models enable us to explore contamination risks and potential outcomes of the contamination-related issues in karst systems. Because of that, they are often used for monitoring, controlling, and managing karst water quality and dependent ecosystem functioning. This paper reviews the current state of knowledge on the modeling of karst transport processes with a focus on single-phase solute transport. By unveiling the fundamental challenges underlying a successful real-world application of karst transport models, we discuss to what extent and how we can handle these challenges. By further deriving the key challenges afront the successful modeling applications in karst systems, we, therefore, provide directions to ensure the reliable modeling of karst transport dynamics in the present context of global changes.