Lung resection surgery, which is performed as a treatment for lung cancer and metastatic lung tumors, is currently conducted via minimally invasive techniques such as video-assisted thoracoscopic surgery and robot-assisted methods. Postoperative complications related to this surgery, such as pulmonary vein thrombosis and cerebral and other organ infarctions, have been increasingly reported. The primary cause of these complications is thrombus formation in the pulmonary vein stump. Statistical data on the site of lung lobectomy have indicated that surgeries involving the left upper lobe are most frequently associated with embolic complications. Although this issue has not received considerable attention in anesthesiology, the importance of prevention and treatment in postoperative management is growing. The role of anesthesiologists in preventing these complications is critical. These roles involve careful fluid management to avoid hypercoagulable states, consideration of early postoperative anticoagulation therapy, assessment of the suitability of epidural anesthesia for postoperative anticoagulation, and improvement of hospital-wide safety systems and monitoring of high-risk patients. Anesthesiologists need to understand the pathology and risk factors involved and play an active role in preventing and treating these complications through effective collaboration with thoracic surgeons and the in-hospital stroke team.