Chronic obstructive pulmonary disease (COPD) and obstructive sleep apnea (OSA) are common diseases that strongly impact the quality and length of life. Their coexistence is determined by overlap syndrome (OS). This systematic review aims to define the significance of these comorbidities according to the current state of knowledge. For this systematic review, we searched PubMed, Scopus, and Cochrane for studies published between 2018 and 26 October 2022, to find original, observational, human studies published in English, where the diagnosis of COPD was according to the Global Initiative for Obstructive Lung Disease guidelines and the diagnosis of OSA was based on polysomnography. The quality of studies was assessed using the Newcastle–Ottawa quality assessment tool for cohort and case–control studies, as well as its modification for cross-sectional studies. Of the 1548 records identified, 38 were eligible and included in this systematic review. The included studies covered a total population of 27,064 participants. This paper summarizes the most important, up-to-date information regarding OS, including the prevalence, meaning of age/gender/body mass index, polysomnography findings, pulmonary function, comorbidities, predicting OSA among COPD patients, and treatment of this syndrome.