We review the proposed mathematical models of the response to osmotic stress in yeast. These models mainly differ in the choice of mathematical representation (e.g. Bayesian networks, ordinary differential equations, or rule-based models), the extent to which the modeling is data-driven, and predictability. The overview exemplifies how one biological system can be modeled with various modeling techniques and at different levels of resolution, and how the choice typically is based on the amount and quality of available data, prior information of the system, and the research question in focus. As a natural part of the overview, we discuss requirements, advantages, and limitations of the different modeling approaches.