In many cases, the surgery results in the death of one or both of the twins, particularly if they are joined at the head or share a vital organ. This makes the ethics of surgical separation, where the twins can survive if not separated, contentious. Alice Dreger of Northwestern University found the quality of life of twins who remain conjoined to be higher than is commonly supposed. Lori and George Schappell and Abby and Brittany Hensel are notable examples. The first record of separating conjoined twins took place in the Byzantine Empire in the 900s. One of the conjoined twins had already died, so the doctors of the town attempted to separate the dead twin from the surviving twin. The result was partly successful as the remaining twin lived for three days after separation. The next case of separating conjoined twins was recorded in 1689 in Germany several centuries later. The first recorded successful separation of conjoined twins was performed in 1689 by Johannes Fatio. In 1955, neurosurgeon Harold Voris (1902-1980) and his team at Mercy Hospital in Chicago performed the first successful operation to separate craniopagus twins (conjoined at the head), which resulted in long-term survival for both. The larger girl was reported in 1963 as developing normally, but the smaller girl was permanently impaired.In 1957, Bertram Katz and his surgical team made international medical history performing the worlds first successful separation of conjoined twins sharing a vital organ.
As of 2015, separation of a genuinely shared heart has not offered survival to two twins; a designated twin may survive if allotted the heart, sacrificing the other twin. Omphalopagus (10%):  Two bodies fused at the lower abdomen. Unlike thoracopagus, the heart is never involved in these cases; however, the twins often share a liver, digestive system, diaphragm and other organs. Parasitic twins (10%): Twins that are asymmetrically conjoined, resulting in one twin that is small, less formed, and dependent on the larger twin for survival. Craniopagus (6%): Fused skulls, but separate bodies. These twins can be conjoined at the back of the head, the front of the head, or the side of the head, but not on the face or the base of the skull.Other, less common types of conjoined twins include:

Cephalopagus: Two faces on opposite sides of a single, conjoined head; the upper portion of the body is fused while the bottom portions are separate. These twins generally cannot survive due to severe malformations of the brain. Also known as janiceps (after the two-faced Roman deity Janus). Syncephalus: One head with a single face but four ears, and two bodies. Cephalothoracopagus: Bodies fused in the head and thorax. In this type of twins, there are two faces facing in opposite directions, or sometimes a single face and an enlarged skull. Xiphopagus: Two bodies fused in the xiphoid cartilage, which is approximately from the navel to the lower breastbone. These twins almost never share any vital organs, with the exception of the liver.