What is the History of foiling in MTG?
Urza's Legacy was the first set to feature foil cards available in booster packs. However, the previous set (Urza's Saga) had a foil prerelease promo card. [Source]

From Urza's Legacy until 8th Edition, the "old-style" foil treatment (with the Wizards of the Coast shooting star across the bottom) was used. The process to create these cards involved a problem where certain foils would include a "cutline": a seam in the foil treatment across the face of the card (see below for an example; the seam runs through the shark in the background).



Details on the modern foil treatment can be found here: Where the Foil Goes.

Note that special releases (e.g., the "From the Vault" series) may use a different foiling process from standard sets. [Source, search for "varnish"]

Additionally, many promos have unique foil treatments, like this Sudden Shock: