Some pairs, depending on the degree of conjunction - in particular, the degree to which they share internal organs - can be separated by surgery. A famous pair, Chang and Eng Bunker (1811-1874), Chinese Americans born in Siam, now Thailand, were known as the Siamese Twins, and this name has often been used as a synonym for conjoined twins.
- Thoracopagus: bodies fused in the thorax (35-40% of cases)
- Omphalopagus: joined at the lower chest (34% of cases)
- Xiphopagous: bodies fused in the xiphoid cartilage, e.g., Chang and Eng
- Pygopagus (illeopagus): joined, usually back to back, to the buttocks (19% of conjoined twins)
- Cephalopagus: heads fused, bodies separated
- Cephalothoracopagus: bodies fused in the head and thorax
- Craniopagus: skulls fused (2%)
In 2003 two women from Iran, Ladan and Laleh Bijani, who were joined at the head but had separate brains (craniopagus) were surgically separated in Singapore, despite surgeons' warnings that the operation could be fatal to one or both. Both women died during surgery on July 8, 2003.