THE dictionary [15] defines a crest as:
1. A tuft, ridge or similar projection on the head of a bird or other animal. 2.a. A plume used as decoration on top of a helmet. b. A helmet. 3. Heraldry. A device placed above the shield on a coat of arms and also used by itself on seals, stationery, and the like. 4.a. The top of something, as a mountain or wave; peak; summit. b. A ridge. 5. The ridge of an animal’s neck or the mane growing on it. 6. Architecture: The ridge on a roof.
When you look at the derivation [16] it becomes even clearer that we are looking at something that belongs on top.
[15] This definition is taken from The American Heritage Dictionary of the English Language (American Heritage/Houghton Mifflin), but I could have taken a definition from any recognised English dictionary.

[16] From Middle English creste, from Old French, from Latin crista, crest, plume.
This also comes from the American Heritage Dictionary, which further traces the origin in an Indo-European rootword.

[17] For the origin of this confusion, see the article Do you have a family crest?

The word occasionally appears in some of the trendier dictionaries with the meaning “a coat of arms” – this is just silly.

The crest is always the topmost part of a coat of arms or armorial achievement (see the entries for these two terms). It cannot by any stretch of the imagination be the whole. [17]

My one quibble with the dictionary definition above is that it describes the crest as being “placed above the shield”, for it is integrally attached to the knight’s helmet.

Bad heraldic design will often show a crest simply sitting on the top of the shield, but properly it is the helmet that should be shown resting on the top of the shield, with the crest attached to it.

Medieval knights would attach the crest to the helmet with bolts. To hide the bolts, a knight would take two (sometimes three, or occasionally four) pieces of silk cord in the principal colours of his shield, twist them around the base of the crest and tie them fast.

This twisted silk, called a crest-wreath or torse, would then appear at the base of the crest.

If the crest is taken on its own (without the helmet) as a symbol of ownership, it always appears with the torse – with two exceptions.

The first exception comes where a crest is defined as issuing (issuant) from a coronet of some kind (usually called a crest-coronet) or perhaps a naval crown (granted to certain distinguished naval families) or a mural crown (various types are found in many civic coats of arms). The coronet or crown is then fixed to the helmet, and the rest of the device comes out of that metal ring.

Such a crest appears with the coronet at its base, instead of a torse.

The second exception in British arms is where the crests of some Scottish barons and of some old English families is placed not on a torse or coronet but on a chapeau or cap of maintenance.

More usually a chapeau is seen inside the coronet of a peer or a sovereign’s crown. But such coronets and crowns are usually displayed on top of the shield, with the helmet and crest above the crown/coronet. (See the large illustration under the entry achievement for an example.)

While the majority of coats of arms in countries following the traditions of Western Europe incorporate crests, there are also many armorial bearings that do not include a crest. The entry for coat of arms gives two examples, both of devices granted by the College of Arms.

However, within Western Europe there is a country that is an exception to the universality of crests: this is France. In the past four centuries or so, crests have almost disappeared from the heraldry of that country, and even families that formerly bore them appear to have forgotten that they ever did.