Obstructive sleep apnea (OSA) is a chronic breathing disorder during sleep that affects 10-30% of adults in North America. The gold standard for diagnosing OSA is polysomnography (PSG). However, PSG has several drawbacks, for example, it is a cumbersome and expensive procedure, which can be quite inconvenient for patients. Additionally, patients often have to endure long waitlists before they can undergo PSG. As a result, other alternatives for screening OSA have gained attention. Speech, as an accessible modality, is generated by variations in the pharyngeal airway, vocal tract, and soft tissues in the pharynx, which shares similar anatomical structures that contribute to OSA. Consequently, in this study, we aim to provide a comprehensive review of the existing research on the use of speech for estimating the severity of OSA. In this regard, a total of 851 papers were initially identified from the PubMed database using a specified set of keywords defined by population, intervention, comparison and outcome (PICO) criteria, along with a concatenated graph of the 5 most cited papers in the field extracted from ConnectedPapers platform. Following a rigorous filtering process that considered the preferred reporting items for systematic reviews and meta-analyses (PRISMA) approach, 32 papers were ultimately included in this review. Among these, 28 papers primarily focused on developing methodology, while the remaining 4 papers delved into the clinical perspective of the association between OSA and speech. In the next step, we investigate the physiological similarities between OSA and speech. Subsequently, we highlight the features extracted from speech, the employed feature selection techniques, and the details of the developed models to predict OSA severity. By thoroughly discussing the current findings and limitations of studies in the field, we provide valuable insights into the gaps that need to be addressed in future research directions.