This study represents a multi-institutional, phase II pilot trial of preoperative chemoradiotherapy followed by surgical resection and postoperative chemotherapy for patients with invasive thymoma or thymic carcinoma at significant risk for recurrence. We hypothesize that this strategy will be well-tolerated and produce response and resectability rates exceeding those previously published involving surgical resection alone, or preoperative chemotherapy followed by surgery. Patients with locally advanced thymoma, based on radiographic and biopsy criteria, will undergo pretreatment computed tomography (CT) scan and positron emission tomography (PET) followed by concurrent (simultaneous) chemotherapy (cisplatin and etoposide) and radiation. After this therapy, patients will be reassessed using computed tomography (CT) and PET, and undergo surgical resection of their tumors. Following resection, patients will be either observed, or treated with postoperative chemotherapy, or chemotherapy and radiation. Correlative genomic, serologic and pathologic studies will also be performed.