Facial reconstruction surgery can be a life-changing procedure for people with facial disfigurement. There are many different types of facial reconstruction surgery, each designed to correct a specific problem. Take a look at some of the most common facial reconstruction procedures. Cleft Lip and Palate Repair Cleft lip and palate are congenital disabilities that cause gaps in the upper lip and roof of the mouth. This repair surgery is often done soon after birth, but it can also be performed later in life.