Obesity and insulin resistance are highly prevalent in subjects diagnosed with sleep apnea. One factor common to obesity, sleep and insulin resistance is autonomic nervous system dysfunction, in particular, sympathetic overactivity. Although the causal links among these factors are not well understood, it is likely that the vicious cycle of interplay among these factors predisposes to the emergence of "metabolic syndrome", a convergence of obesity, hypertension, insulin resistance and dyslipidemia that is appearing in epidemic proportions in the United States and other countries. This chapter provides an overview of the ongoing experimental and modeling studies in my laboratory aimed at elucidating and quantifying the relationships among autonomic dysfunction, insulin resistance and severity of sleep apnea in overweight subjects. These studies employ a "minimal modeling" approach to extract information characterizing autonomic function from noninvasive cardiorespiratory measurements. We subsequently determine the relationship of these model parameters to the parameters estimated from the Bergman minimal insulin-glucose model using data obtained from the frequently sampled intravenous glucose tolerance test performed on the same individuals.