Recent studies have uncovered high prevalence of undiagnosed sleep-disordered breathing, and its linkage to metabolic or cardiovascular disorders which represent increasing health hazard. However, the mechanistic links behind these disorders as well as their contribution to the experimental observations and treatment responses remain poorly understood. Therefore, the screening of clinical measurements still relies upon relatively simple diagnostic features, such as signal averages or event frequencies, which may represent suboptimal or surrogate markers of the underlying abnormality. Consequently, most patients are being treated with general therapies regardless of the cause of their key dysfunction. Combining experimental measurements with mathematical modelling has the potential to provide mechanistic insights into the individual factors underlying the disease progression, which may finally enable tailored treatment alternatives for each patient. This review depicts a number of modelling approaches to elucidate sleep-related dysfunctions of the human respiratory system, and how these models are being used to translate the measurements first into new ideas and then into testable hypotheses. Such model-based investigations can provide systematic strategies towards better understanding, predicting or even preventing these dysfunctions. Along with the brief description of the modelling approaches, we discuss their relative merits and potential implications especially for clinical research.