The traditional approach to mediastinal cyst and mass resection has been open via median sternotomy or thoracotomy. With the advent of minimally invasive techniques, there have been successful cases completed via video-assisted thoracoscopic (VATS) and robot-assisted thoracoscopic surgery (RATS). Although mediastinal cysts are uncommon, they are a significant and relevant topic in the practice of thoracic surgery. Thus, this clinical practice review aims to summarize and highlight some of the key case series and retrospective studies in order to provide insight on each of the approaches. In addition, there is a brief review of other approaches, such as subxiphoid, and the utility of endobronchial ultrasound in the management of mediastinal cysts. In this review, the identified benefits of VATS and RATS lie largely in quality improvement of the patient experience—decreased length of stay (LOS) and pain—without compromising patient outcomes. However, the open approach remains a viable option, particularly for the management of large cysts or as a bail-out option. When surgeons approach with VATS or RATS and encounter bleeding or difficult dissection planes, it is consistent in the literature that conversion to thoracotomy is the safe next step. Our clinical practice is to attempt VATS or RATS approach for mediastinal cysts when possible. The data used for this review relies heavily on case reports and case series, and thus is the main limitation of this clinical practice review.