Summon

Summoning is the process by which a magic-user calls forth or "summons" a creature to do their bidding.

Prerevisionist
Summoning in prerevisionist material was the literal movement of a being to the presence and control of the mage or planeswalker summoning it. Some summoned creatures agreed to be servants of the spellcaster, while others were enslaved by the spell known as the geas, to be used in magical combat. If the wizard doing the summoning was victorious, the summoned creatures were usually returned to their places of origin; but if the wizard failed, the surviving summoned creatures would be stranded where they were summoned.

Revisionist
The modern idea of summoning involves both the prerevisionist way and the creation of a faux entity based on the concept of that creature, which is pulled from the aether. These summoned creatures have no will of their own and vanish when no longer needed. This concept is described in The Eternal Ice by Lim-Dûl to Jodah. Though Jodah is not in fact summoned, as Lim-Dûl suggests, the explanation is still valid. The short story Loran's Smile further elaborates upon this summoning model and shows it firsthand. Feldon learns how to summon from a scholar who says to study him for two weeks; after the two weeks have passed, Feldon is able to understand what makes this scholar a scholar and is able to summon this concept of a scholar as a creature.

The summoning of unique, legendary individuals is similar to this, but based on the concept of a specific individual and not simply off of a group. Loran's Smile also elaborates on this distinction: Feldon's summoned copy of his mentor only stems from the concept of a scholar, resulting in a creature with various physical differences from the original, but he is able to summon a perfect copy of his late lover Loran by recalling his memories with her.

Planeswalkers can only summon creatures they've personally interacted with so that obviously limits them to creatures from planes they've visited. Ordinary wizards can therefore only summon creatures from their own plane.

Some modern stories operate on a pre-revisionist model of summoning, however. For instance, Kiora summoned Lorthos across Zendikar, and Ugin stripped Nicol Bolas of his names to prevent summoning him from the Meditation Realm.

Summoned creatures leave corpses when they are killed, though they can also simply fade away when their summoners lets the summoning spell lapse.

Other Creature Spells
Other types of spells have been depicted giving mages creatures under their control. It is unclear if these other spells count as "summoning". They include creating illusions, creating elementals from the surrounding natural resources, using necromancy to raise the undead, and magically taking control of animals in the surrounding area. This last method has been referred to as "summoning" in the past.

In-game
A Summon spell, Summon Creature, or Summon is an obsolete card type which had the form of "Summon " in the type line of a card (where would be the current creature subtype). In the Sixth Edition rules changes, it was replaced with the card type "creature".

If a spell was a Summon Spell it would indicate what class of creature [was] being summoned.

Summoning was the act of casting a card. Once the card was played it was no longer considered a spell, but represented a permanent creature of the mentioned type. After it was cast, that creature would have summoning sickness.

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Trivia

 * "Summon" reappeared as a specter of the past on the Mystery Booster test card Xyru Specter. The Release notes specifically note that Summon isn't a card type.