Source: Yugioh Wikia
Special Summon-only monsters (often incorrectly referred to as Semi-Nomi monsters) are monsters with the text "This card cannot be Normal Summoned or Set. This card can only be Special Summoned...". If a monster is a Special Summon only monster, then it means it must be Special Summoned by its listed effect before it can be Special Summoned by another effect. "Aqua Spirit", "Harpie Lady Sisters", and "Black Luster Soldier - Envoy of the Beginning" are all Special Summon only monsters.
After a Special Summon only monster has been Special Summoned properly, it can be Special Summoned through other effects. This only lasts as long as the monster does not return to the hand or Deck. As long as the monster remains on the field, in the Graveyard, or removed from play, you can Special Summon it again with other card effects.
- A player removes from play three Fiend-type monsters to Special Summon "Dark Necrofear". If it is destroyed and sent to the Graveyard, it can be revived with cards such as "Monster Reborn".
- If, afterwards, it is removed from play by "Dark Core", you can still Special Summon it with cards such as "Dimensional Inversion".
- If after all this, "Dark Necrofear" is returned to the Deck or hand (such as by "Phoenix Wing Wind Blast" or "Compulsory Evacuation Device"), then you must remove three Fiends to Special Summon "Dark Necrofear"'s again. You cannot Special Summon it from the hand or deck by other cards, such as "Monster Gate" or "Doom Shaman".
- If it is later removed from play or sent to the Graveyard (such as by "Graceful Charity"), it still cannot be Special Summoned.
Note that Fusion Monsters, Ritual Monsters and Synchro Monsters are treated as Special Summon only monsters, unless stated otherwise. Also unless stated otherwise, Fusion Monsters are properly Special Summoned by a Fusion Summon, Ritual Monsters are properly Special Summoned by a Ritual Summon, and Synchro Monsters are properly Special Summoned by a Synchro Summon.
There is also a sub-type of monsters called "Nomi".