Sleeve

A sleeve (O. Eng. "slieve", or "slyf", a word allied to "slip", cf. Dutch "sloof") is the part of a garment that covers the arm, or through which the arm passes or slips. The pattern of the sleeve is one of the characteristics of fashion in dress, varying in every country and period. Various survivals of the early forms of sleeve are still found in the different types of academic or other robes. Where the long hanging sleeve is worn it has, as still in China and Japan, been used as a pocket, whence has come the phrase "to have up one's sleeve", to have something concealed ready to produce. There are many other proverbial and metaphorical expressions associated with the sleeve, such as "to wear one's heart upon one's sleeve", and "to laugh in one's sleeve".
Sleeve length varies from barely over the shoulder ("cap sleeve") to floor-length. Most contemporary shirt sleeves end somewhere between the mid-upper arm and the wrist.
Early medieval sleeves were cut straight, and underarm triangle-shaped gussets were used to provide ease of movement. In the 14th century, the rounded sleeve cap was invented, allowing a more fitted sleeve to be developed.
History.
Middle Ages.
The medieval sleeve or set-in sleeve was unlike modern techniques. The seam for this type of sleeve was usually placed at the back of the arm, and fit under the arm. 
Types of sleeves.
Often the names applied to sleeves in historical costume are modern.