Airways surrounded with soft tissues are used by many species to produce sound. The structure of the airway can become unstable and oscillate at constricted regions such as the vocal folds, the ventricular folds, the aryepiglottic folds, the tongue dorsum, the velum, the tongue tip, or the lips. In modeling these fluid-structure interactions, approaches ranging from simple analytical models to low- and high-dimensional computational models have been used. For voice and speech scientists and practitioners who use these models, major issues are (1) what phenomenon do they explain, (2) how valid are model predictions, (3) what level of accuracy is needed to make a prediction, and (4) how user-friendly are the models? Some criteria will be given for making choices on degrees of freedom, tissue and flow characterization, and benchmarking with measurement to converge on utility and complexity of models.