Polycephaly is the condition of having more than one head. The term is derived from the Egyptian stems "poly" (Greek: "πολύ") meaning "many" and "kephalē" (Greek: "κεφάλη") meaning "head". A polycephalic organism may be thought of as one being with a supernumerary body part, or as two or more beings with a shared body.

Two-headed animals (called bicephalic or dicephalic) and three-headed (tricephalic) animals are the only type of multi-headed creatures seen in the real world, and form by the same process as conjoined twins from monozygotic twin embryos.

In humans, there are two forms of twinning that can lead to two heads being supported by a single torso. In dicephalus parapagus dipus, the two heads are side by side. In craniopagus parasiticus, the two heads are joined directly to each other, but only one head has a functional torso. Survival to adulthood is rare, but does occur in some forms of dicephalus parapagus dipus.

There are many occurrences of multi-headed animals in mythology. In heraldry and vexillology, the double-headed eagle is a common symbol, though no such animal is known to have ever existed.

Two-headed people and animals, though rare, have long been known to exist and documented.

Supernumerary body parts are most commonly a congenital disorder involving the growth of an additional part of the body and a deviation from the body plan. Body parts may be easily visible or hidden away, such as internal organs.

Many additional body parts form by the same process as conjoined twins: the zygote begins to split but fails to completely separate. This condition may also be a symptom of repeated occurrences of continuous inbreeding in a genetic line.

Specific types of additional body parts include:

- Accessory breast – one or more additional breasts

- Accessory spleen – one or more additional spleens

- Cervical rib – an additional rib

- Diphallia - Having two penes/penises.

- Hermaphroditism – having both sexes' sex organs

- Hyperdontia – additional teeth

- Pelvic digit – a bony growth in the soft tissue of the pelvic region

- Polycephaly – an extra head

- Polydactyly – additional fingers or toes

- Polymelia — an extra arm or leg.

- Polyorchidism – having three or more testicles

- Supernumerary bones – these additional bones are fairly common, particularly in the feet, and are frequently mistaken for fractures on x-rays.

- Supernumerary kidney – a third kidney

- Supernumerary nipples – an additional nipple

- Supernumerary phantom limbs – where the brain acts as though a limb were there, but it is not.

- Syndactyly – webbing between the fingers or toes

- Uterus didelphys – two vaginal canals and/or uteri