Obstructive sleep apnea (OSA) is a highly prevalent disease characterized by recurrent closure of the upper airway during sleep. It has a complex pathophysiology involving four main phenotypes. An abnormal upper airway anatomy is the key factor that predisposes to sleep-related collapse of the pharynx, but it may not be sufficient for OSA development. Non-anatomical traits, including (1) a compromised neuromuscular response of the upper airway to obstruction, (2) an unstable respiratory control (high loop gain), and (3) a low arousal threshold, predict the development of OSA in association with anatomical abnormalities. Current therapies for OSA, such as continuous positive airway pressure (CPAP) and oral appliances, have poor adherence or variable efficacy among patients. The search for novel therapeutic approaches for OSA, including pharmacological agents, has been pursued over the past years. New insights into OSA pharmacotherapy have been provided by preclinical studies, which highlight the importance of appropriate use of animal models of OSA, their applicability, and limitations. In the present review, we discuss potential pharmacological targets for OSA discovered using animal models.