Centaurs.

Centaurs have the body of a horse but the head and torso of a human. In Greek myth most centaur were considered the Centaurs descendants of the Magnesian Mares and Centaurus, himself the son either of Ixion and Nephele or Apollo and Stilbe (accounts vary),

The word centaur is derived from the words κεντέω (to hunt), ταῦρος (a bull). This may relate to the people of Thessaly who hunted bulls from horseback. Their ability might somehow have been linked to or confused with centaurs who were also often said to live on Thessaly.

• Hippocentaur--other prefixes would mark being half-man and half another species. For example bucentaur would be a man-ox. (By contrast the 'androcephalous' would be a man's body with a horse's head.)
  
• Kéntauroi (male), kentaurides (female).
  

Centaurs are frequently represented in heraldic crests. The centaur represents various traits such as valor in battle and warfare. It may also serve as a general symbol of vitality or virility.

Because of the combination of human and animal, the centaur is often used to represent veterinary medicine.

The most famous centaur legend relates to how the centaurs behaved when they attended the wedding feast of the Lapith Pirithious. After drinking too much wine they became unruly and a battle broke out. The hero Theseus fought for the Lapiths and they triumphed over the centaurs. The centaur leader, who had attempted to assault the bride had his ears and nose cut off in punishment.

This battle is famously depicted on the Elgin marble metope from the Parthenon currently held in the British Museum (London, UK). Many other artists have depicted this battle, including Michelangelo.

Early centaur tales mention only males, but later mention was made of kentaurides, female centaurs.

In accounts of the battle between the centaurs and the Lapiths only one female centaur is mentioned as being present, Hylonome. When her husand Kyllaros was killed in the battle she committed suicide using his spear.

Hylonome is described by Ovid as follows: "In the high woods there was none comelier of all the centaur-girls, and she alone by love and love’s sweet words and winning ways held Cyllarus, yes, and the care she took to look her best (so far as that may be with limbs like that). She combed her glossy hair, and twined her curls in turn with rosemary or violets or roses, and sometimes she wore a pure white lily. Twice a day she bathed her face in the clear brook that fell from Pagasae’s high forest, twice she plunged her body in its flow, nor would she wear on her left side and shoulder any skin but what became her from best-chosen beasts."

Chiron the centaur was the wise teacher, healer and mentor of many heroes from Greek myth including Asklepios, Jason and Peleus.

Pholos was a centaur who hosted Hercules when he was searching for the Erymanthian boar.

The story goes that when the centaur Chiron was accidentally killed by one of Hercules arrows Zeus placed him in the sky as a constellation. In astrology, Sagittarius is the ninth sign of the zodiac. The name of the constellation is derived from the Latin, sagitta, meaning 'archer'--as the centaur is depicted drawing a bow.

Centaurs appear in advertisements for Old Spice and In print advertisements for Chile Fashion Week (2007).

Centaurs serve as mascots or symbols for the fraternity Delta Lambda Phi and the Preakness.

The Saune Centaur (137AD)

Phlegon of Tralles described seeing an embalmed Centaur in the storehouse of the Emperor Hadrian: "At first it was shown in the palace. Its face was more savage than a human face, its arms and its fingers were hairy and its ribs were joined to its front legs and its stomach. It had strong hooves of a horse and its mane was tawny. However, because of the embalming process its mane and its skin had become dark. In terms of its size it was not as usually shown, but it was not much smaller either."

These days even the most ardent cryptozoologist is unlikely to suggest that centaurs really exist, or ever did.  Partly because, unlike many other cryptids, they just don't make a lot of biological sense.

Perhaps the best simulated centaur can be found at the John C. Hodges Library at the University of Tennessee. They display a full centaur skeleton unearthed in the "Centaur Excavations at Volos".

A simulated photograph of a centaur skeleton was created by Three Prongs.

Detailed speculative anatomy for centaurs has been created in order to produce computer-generated centaurs with realistic appearance and movement for movies such as The Lion, the Witch and the Wardrobe.

John Howe created some imaginary medieval centaur armor.

Sculpture

Centaurs are particularly popular subjects for modern sculptors. For example Joe Warren created a centaur archer out of recycled spare parts and junk metal. And Ron Rodgers creates centaurs with long spindly legs. Sculpture Alley has an odd body builder centaur that you can have inscribed.

• The Segway Centaur [concept vehicle]
• Any of a group of icy bodies similar to both asteroids and comets, orbiting the Sun in elliptical paths mostly in the region between Saturn and Neptune is also referred to as a centaur.

Kalki

A destructive avatar of Vishnu, Kalki, is something depicted as a horsed headed centaur.

Winged (Pterocentaur)

Winged centaurs appear in the Xanth novels by Pier Anthony.

And also some more modern variants:

• Insectoid Centaur Barbie Fighting Robot

Some modern material shows human-taurs where the hind part is made up of human legs and extra human buttocks and possibly torso. But be aware that quite a lot of this material is explicit and/or fetishistic.

However what most people may not know that many ancient depictions of centaurs gave them human front legs and same gave them human fore and hind legs.

Dolls

Several types of centaur doll are made including: Gem and Shimmers.

Also there are official centaur action figures television such as Hercules and movies such as Narnia and Harry Potter.

Other centaurs have be created from standard doll types.

• Debrohun, JB (2004). Centaurs in Love and War: Cyllarus and Hylonome in Ovid Metamporphoses. American Journal of Philology125, 417-452. [Abstract]