Mediastinal tumors are a remarkably diverse category. They include malignant and benign forms with different rates of disease progression and tissue invasion. Anesthesiologists may encounter significant difficulties in managing patients with giant mediastinal tumors due to the non-negligible occurrence of severe cardiorespiratory collapse. Respiratory complications ensue from the compression of the airways induced by the mediastinal mass: the compressive effects may be exacerbated by positioning or anesthesia induction. Furthermore, the compression or invasion of major vessels may elicit acute cardiovascular collapse. The specter of sudden cardiorespiratory deterioration should lead the anesthesiologist to careful planning: acknowledging clinical and radiological signs that may presage an increased risk of life-threatening complications is of pivotal importance. This review aims to present a strategy for treating patients with mediastinal masses, starting with the pathophysiological elements and moving through preoperative care, intraoperative behavior, and the recovery period. We will also focus on respiratory and cardiovascular issues, emphasizing the need for extracorporeal membrane oxygenation (ECMO) as a rescue and crucial component of the anesthesia strategy. Understanding the physiological alterations after anesthesia induction can aid in identifying and treating potential problems. In addition, we attempted to offer insight into multimodal anesthesia and analgesia management: we emphasize the importance of a thorough preoperative assessment and the need for reviewing extracorporeal support not just a resuscitative strategy but as an integrated component of the perioperative care.