Morph

Morph is a keyword ability on permanents that allows the player to pay to cast a card with the ability face down as a 2/2 colorless, typeless creature. The player can then turn that creature face-up at any time they could cast an instant by paying a variable Morph cost printed on each card. Many permanents with morph have additional triggered abilities that trigger when they are turned face-up (see Bane of the Living), and some other permanents trigger when a different card is turned face up. Morphing doesn't use the stack.

History
Morph came about because the rules team was trying to figure out a way to make Illusionary Mask and Camouflage work. The answer was to define face-down cards as creatures with a power and toughness. The rules team realized the solution led to a mechanic. Cards could be cast face-down and then, for a cost, could be later turned face-up. As all face-down creatures were the same, it would create a sense of mystery. The rules team pitched the idea to Mark Rosewater, who loved it. The ability first appeared in Onslaught block    and was revisited in the Time Spiral block. Most morph creatures in these sets had a visual cue in their art that represented the mysteriously uniform “morph shell” from which the morph creature emerges. It's that spider-shaped creature shell that is represented in Onslaught’s expansion symbol. These "clay spiders" can be seen in the art for Dermoplasm and several other cards.

Morph returned again in Khans of Tarkir. The mechanic was now visually represented as a swirl of draconic magic, used as a disguise. Fate Reforged, The second set of the Khans of Tarkir block featured manifest, the proto-morph from Tarkir's past. Morph, megamorph and manifest all reappeared in Commander 2019.

"Borph", "Smorph" and "Auramorph"
For a while, an alternate version of morph was considered for the design of Khans of Tarkir. This new mechanic was very similar but instead of three mana to cast the 2/2 face-down creature it cost two mana. R&D nicknamed that mechanic "borph" as in "bear morph" because Bears are slang for a vanilla 2/2. Other options that were looked at were "Smorph"(4 for a facedown 2/2 with a +1/+1 counter) and "Auramorph" (3 for a facedown 2/2 that's an aura on the backside).

Auramorph was realized in Commander 2019 with Gift of Doom.

Spellmorph
Spellmorph, that can appear on Instants and Sorceries, first appeared on a test card in the Mystery Booster set (You may cast this card face down as a 2/2 creature for . Cast it any time for its spellmorph cost).

Megamorph
undefined Dragons of Tarkir introduced megamorph, as an alternate  evolution of Manifest. Megamorph creatures are basically morph creatures with one extra bonus. Turning them face-up by paying their megamorph cost puts a +1/+1 counter on the creature. Often the cards have an additional beneficial effect that is only activated when the megamorph cost has been paid.

Megamorph was also used in Commander 2019.

Rulings

 * Morph lets you cast a card face down by paying and lets you turn the face-down permanent face up any time you have priority by paying its morph cost.
 * The face-down spell has no mana cost and has 0 mana value. When you cast a face-down spell, put it on the stack face down so no other player knows what it is and pay 3. This is an alternative cost.
 * When the spell resolves, it enters the battlefield as a 2/2 creature with no name, mana cost, creature types, or abilities. It's colorless and has 0 mana value. Other effects that apply to the creature can still grant it any of these characteristics.
 * Any time you have priority, you may turn the face-down creature face up by revealing what its morph cost is and paying that cost. This is a special action. It doesn't use the stack and can't be responded to. Only a face-down permanent can be turned face up this way; a face-down spell cannot.
 * If a face-down creature loses its abilities, it can't be turned face up by paying its morph cost because it no longer has morph or a morph cost.
 * Because the permanent is on the battlefield both before and after it's turned face up, turning a permanent face up doesn't cause any enters-the-battlefield abilities to trigger.
 * Because face-down creatures don't have a name, they can't have the same name as any other creature, even another face-down creature.
 * A permanent that turns face up or face down changes characteristics but is otherwise the same permanent. Spells and abilities that were targeting that permanent, as well as Auras and Equipment that were attached to the permanent, aren't affected.
 * Turning a permanent face up or face down doesn't change whether that permanent is tapped or untapped.
 * At any time, you can look at a face-down spell or permanent you control. You can't look at face-down spells or permanents you don't control unless an effect instructs you to do so.
 * If a face-down spell leaves the stack and goes to any zone other than the battlefield (if it was countered, for example), you must reveal it. Each graveyard is kept in a single face-up pile.
 * If a face-down permanent leaves the battlefield, you must reveal it. You must also reveal all face-down spells and permanents you control if you leave the game or if the game ends.
 * You must ensure that your face-down spells and permanents can easily be differentiated from each other. You're not allowed to mix up the cards that represent them on the battlefield in order to confuse other players. The order they entered the battlefield should remain clear. Common methods for doing this include using markers or dice, or simply placing them in order on the battlefield.

Megamorph rulings

 * Turning a face-down creature with megamorph face up and putting a +1/+1 counter on it is a special action. It doesn't use the stack and can't be responded to.
 * If a face-down creature with megamorph is turned face up some other way (for example, if you manifest a card with megamorph and then pay its mana cost to turn it face up), you won't put a +1/+1 counter on it.
 * With the exception of putting a +1/+1 counter on the creature as it turns face up, megamorph functions the same way morph does.

Overlay card
Khans of Tarkir introduced the Morph-overlay card which was available in booster packs as an extra card with an advertisement on the back side. The overlay card may be used on face-down Morph cards to remind players of their power and toughness and that it can be turned face-up for its Morph or Megamorph cost.

Cards that interact with morph

 * Exiled Doomsayer
 * Dream Chisel
 * Obscuring Aether
 * Qarsi Deceiver</c>
 * Backslide</c>

Non-creature cards with morph

 * The first non-creature cards with morph were Lumithread Field</c> (an enchantment), Whetwheel</c> (an artifact) and Zoetic Cavern</c> (a land). Commander 2019 would later add a aura in the form of Gift of Doom</c>.
 * As soon as a non-creature card with morph is turned face up, it stops being a creature. Any Equipment attached to it fall off. Any Auras that can't be attached to it fall off. Any counters that are on it will remain, though they might not have any effect.
 * If such a permanent is in combat when it's turned face up, it's removed from combat. Combat damage that it assigned will not be dealt. Combat damage assigned to it will not be dealt. This is because the permanent is removed from combat when it stops being a creature. As such, it is removed from all damage assignment orders. Blockers do not assign any damage if no attackers are assigned to it.
 * Three Onslaught block cards (Aphetto Runecaster</c>, Aven Farseer</c>, and Bonethorn Valesk</c>) are printed with abilities that trigger whenever a creature is turned face up. These are erratad so they trigger whenever a permanent is turned face up.

Cards referring to morph
Four older cards used to refer to a creature or a creature card "with morph." After the introduction of Megamorph this became "with a morph ability".
 * Backslide</c>
 * Dermoplasm</c>
 * Master of the Veil</c>
 * Weaver of Lies</c>