Special Summon (特殊召喚 Tokushu Shōkan) is any Summon other than Normal Summon or Flip Summon. They usually occur due to a card effect or Summoning condition. The monster is played directly onto the Monster Card Zone in face-up Attack Position or face-up Defense Position, unless the card indicates otherwise; unlike Normal and Flip Summons, monsters can be Special Summoned face-down (but only when a card specifically says so). Ritual Summons, Fusion Summons, Contact Fusions, Synchro Summons and Xyz Summons are all Special Summons.
Special Summons do not take up the player's Normal Summon/Set for the turn, and there is no restriction on the number of times they can be performed in a turn. Special Summoning does not require Tributes for high-Level monsters like Normal Summons and Sets do, unless otherwise specified by a card.
Special Summon groups
There are two different groups that describe how monsters are Special Summoned. The group affects which cards can negate the Special Summon.
Cards printed with Problem-Solving Card Text can easily have their method of Special Summon determined; cards whose effect to Special Summon themselves that contain colons or semicolon are Special Summons due to a card effect, whereas cards that Special Summon themselves that don't contain either are built-in Special Summons. Any card effect that Special Summons a different card is a "Special Summon with a card effect".
Built-in Special Summons
Built-in Special Summons (also known as inherent Special Summons) are Special Summons that happen due to a Summoning condition that the monster has; this Special Summon does not start a Chain. This can only be performed when the game state is open during your Main Phase (for example, "Cyber Dragon", "Solar Wind Jammer", "Ghost Ship", "Exodius the Ultimate Forbidden Lord", etc.). This type of Special Summon behaves similarly to Normal Summons and Flip Summons. Contact Fusions, Synchro Summons and Xyz Summons (except Rank-Ups) fall into this group of Special Summons.
Following the Problem-Solving Card Text, monsters' card text will specify in parenthesis "()" the location from which they can be Summoned, excluding Synchro and Xyz Summons. Monsters whose card texts do not specify the location from where they are Summoned are always Summoned from the hand if they are used in the Main Deck, and from the Extra Deck if they are used there.
These Special Summons are the only Special Summons that have a Summon negation window. As such, they can be negated by any card that can negate Special Summons, including "Solemn Warning", "Solemn Judgment", and "Black Horn of Heaven". Cards such as "Divine Wrath" cannot negate this type of Special Summon, because they do not start a Chain.
However, not all monsters that can Special Summon themselves do so as a built-in Special Summon; some monsters have effects that Special Summon themselves but start a Chain, such as "Andro Sphinx".
Special Summon with a card effect
These are any Special Summon that results or occurs at the resolution of an activated card effect that Special Summons (e.g. "Monster Reborn" and "Gorz the Emissary of Darkness"). Fusion Summons, Ritual Summons and Rank-Ups fall under this group of Special Summons.
These Special Summons cannot be negated, but they can be stopped by negating the initial effect that caused the Special Summon. Cards such as "Black Horn of Heaven" and "Thunder King Rai-Oh" cannot negate this Special Summon, because it occurs during resolution of a card effect. However, cards such as "Divine Wrath" and "Dark Bribe" can negate the activation of a monster effect or Spell/Trap Card that would Special Summon a monster, respectively. "Solemn Judgement" can negate either a Spell/Trap effect (including one that would Special Summon a monster) or a built-in Special Summon; however, it cannot negate monster effects that Special Summon. "Solemn Warning" can negate any effect that Special Summons, as well as built-in Special Summons (if it is a Spell or Trap card, "Solemn Warning" can only negate it if it is the initial activation of the card as it cannot negate activation of effects).
Summon response window
Cards and effects that can be activated in response to a successful Special Summon, such as "Torrential Tribute" and "Bottomless Trap Hole", can be activated after any of these Special Summons, regardless of whether it is built-in or because of a resolved effect. However, they cannot be activated if a monster is Special Summoned by a card effect that is Chain Link 2 or higher, unless the activation of all other cards and effects that would resolve after it are negated. This is because cards and effects cannot be activated in the middle of a resolving Chain, and whatever effect resolves last (as Chain Link 1) would cause these cards to miss the timing.
Furthermore, if the card effect that Special Summoned the monster did something else immediately after Special Summoning the monster (e.g. "Magical Dimension"), then this window does not occur and any cards that can be activated in response to a Summon miss the timing.