Complex sleep apnea entails the combination of obstructive and central sleep apnea during the same polysomnographic study. Treatment-emergent central sleep apnea during administration of positive airway pressure for obstructive sleep apnea is the most common form of complex sleep apnea. In most cases of treatment-emergent complex sleep apnea without cardiovascular comorbidity or opioid use, the central component may resolve with use of continuous positive airway pressure sufficient to eliminate the obstructive component. Effective treatment of persistent complex sleep apnea can be achieved with the use of adaptive servoventilation.