Mathematical and computational modeling is critical to advancing our understanding of structure-function relationships in the lung. Systems of coupled ordinary differential equations are used to describe the behavior of interacting lung compartments and are readily solved either analytically or numerically, but they have limited spatial resolution. Systems of partial differential equations describe behavior that is continuous both in time and space. Agent-based models are computationally expensive but have the advantage of representing reality more or less as we perceive it, making this type of modeling more accessible to biomedical scientists without strong mathematics backgrounds. Forward models, used for simulation, are implemented by a priori selection of model structure and parameter values, and may be highly complex. In contrast, inverse models, which are used to infer what may be taking place within a system from observed relationships between inputs and outputs, must have few adjustable parameters. Multiscale models account for phenomena that arise at different levels of length and/or time scale and are crucial for understanding the emergent behavior that appears ubiquitously in biology. Importantly, a model must be validated in terms of its usefulness for the task at hand.