Esophageal atresia (EA) is a rare and complicated congenital malformation. Since it was first reported, it has had a long history. Nowadays, standard treatment options consist of open procedure and thoracoscopic surgery. Each procedure has its benefits and defects, and the relative merits of both methods are still debated. We conducted a systematic literature review on the surgical repair of the EA, from the first descriptions of EA with tracheoesophageal fistula (TOF) appeared in the 19th century to 2018. The opening and the laparoscopic surgery are the two effective methods to deal with the EA, and they all have their benefits and some aspect to be improved. The main complications for the operation were anastomotic leakage, anastomotic stenosis and recurrence of TOF. Results indicate that the patients of opening surgery were more likely to have leakage, but these patients also showed a lower stenosis rate than the thoracoscopy patients. Meanwhile, the rate of recurrence for TOF had no statistical difference between the procedure types. Thoracoscopic surgery was beneficial and promoted a good prognosis in EA patients when compared to open surgery, although there is still more research to be done in this regard.