XYZ Monsters are a type of Monster Card. The first XYZ was released in Starter Deck Dawn of the XYZ. These are black Cards which are placed in the Extra Deck.
Properly Special Summoned
To be properly Special Summoned, XYZ Monsters must first be XYZ Summoned. If they leave the Extra Deck without being XYZ Summoned, they cannot be Special Summoned.
Cannot exist in the Hand
Like other Extra Deck Monsters, XYZ Monsters cannot exist in the hand or Main Deck. If a XYZ Monster would be moved to the hand or Main Deck, it is returned to the Extra Deck instead.
XYZ Monsters do not have Levels, and instead have a Rank. A XYZ Monster's Rank determines the required Levels of the XYZ Materials needed in order to XYZ Summon it. A XYZ Monster's Rank is illustrated by a row of yellow stars in black circles (as opposed to the yellow stars in red circles used to illustrate a Monster's Level).
Because they do not have Levels, you cannot use XYZ Monsters for Ritual, Synchro, or XYZ Summons (unless otherwise specified). Effects that depend on a Monster's Level, such as "Burden of the Mighty", have no Effect on XYZ Monsters.
A XYZ Summon is the act of Summoning a XYZ Monster from the Extra Deck using 2 or more face-up Monsters of the same Level from your field as XYZ Materials. Those Monsters have to be the same Level as the XYZ Monster's Rank.
During your Main Phase, you can XYZ Summon an XYZ Monster from your Extra Deck. When an XYZ Monster is XYZ Summoned, the XYZ Materials are stacked and placed underneath the XYZ Monster.
To perform an XYZ Summon, two or more Monsters with the same Level must be used as the XYZ Materials. Token Monsters cannot be used as XYZ Materials. Monsters that do not have Levels (such as XYZ Monsters and Link Monsters) cannot be used as XYZ Materials unless specifically permitted (such as by "Number S0: Utopic ZEXAL"). While the majority of the XYZ Monsters require two XYZ Materials, many XYZ Monsters require more or can use a variable number of Materials.
While attached to an XYZ Monster, XYZ Materials are not treated as being on the Field. Cards being attached as an XYZ Material or used as an XYZ Material in an XYZ Summon are not considered to be leaving the Field.
If an XYZ Monster is no longer on the Field, its XYZ Materials are sent to the Graveyard. XYZ Materials remain attached if an XYZ Monster is flipped face-down.
Several XYZ Monsters can be Special Summoned by XYZ Evolution, a kind of Special Summon treated as an XYZ Summon. XYZ Evolution allows an XYZ Monster to be Special Summoned using another XYZ Monster as its XYZ Material. The Materials of that XYZ Monster are transferred and attached to the Summoned XYZ Monster.
Unless stated specifically (like in most cards that perform XYZ Evolution) that the XYZ Materials will be transferred to the new XYZ Monsters, if an XYZ Monster is used in XYZ Summon (Such as due to the Effect of "Xiangke Magician"), the XYZ Materials will be sent to the Graveyard.
"Rank-Up Magic" Spell Cards can perform an XYZ Evolution, Special Summoning an XYZ Monster with a higher Rank than the original XYZ Monster.
Usually, Rank-Up XYZ Evolution Summons an XYZ Monster one Rank higher than the preceding Monster, but some Cards Summon XYZ Monsters two Ranks higher.
The Spell Cards "Rank-Down-Magic Numeron Fall" and "Rank-Down-Magic Utopia Fall" perform an XYZ Evolution, Special Summoning an XYZ Monster with a lower Rank than the original XYZ Monster.