The occurrence of extremely thin liquid-sided concentration boundary layers at bubble or droplet interfaces for realistic, i.e., high Schmidt numbers is a severe obstacle for the numerical simulation of mass transfer processes in gas-liquid systems. This contribution provides a survey of different approaches to overcome this problem, with the main emphasis put on the approach introduced and further developed by the authors. This approach employs a nonlinear flux computation and is based on the modeling of subgrid-scale concentration profiles. Based on the latest developments, recommendations for future research are also provided.