Most monsters can be summoned without any restrictions, even if you might have to tribute monsters to summon them. However, some monsters have special summoning restrictions. Usually, you have to fulfill certain requirements to summon the card. While this can be quite a drawback, most of these monsters have powerful effects to make up for it. There are two types of monsters with summoning conditions; nomi monsters and semi-nomi monsters.
Nomi MonstersA Nomi monster will have one of two very specific phrases in its card text:
"This card cannot be Normal Summoned or Set. This card cannot be Special Summoned except...", followed by a summoning condition, for cards printed before Problem-Solving Card Text.
"Cannot be Normal Summoned or Set. Must be Special Summoned..." followed by a summoning condition, "... and cannot be Special Summoned by other ways", for cards printed after Problem-Solving Card Text.
Examples include the "Berserk Dragon" pictured here, "Dark Armed Dragon", and "Doom Dozer". A Nomi monster's summoning conditions are not always difficult to fulfill; examples include "Aztekipede, the Worm Warrior" and "Yamato-no-Kami"; they simply require the removal of a certain type of monster from your grave. However, most Nomi monsters are difficult to summon.
One very important thing about Nomi monsters is that they cannot be special summoned in any way except how it is specified. For instance, if you summon Dark Armed Dragon and it is destroyed, you cannot special summon it from the graveyard with Monster Reborn. To re-summon it, you have to add it back to your hand, and then re-fulfill the summoning requirements.
In addition to these effect monsters, Fusion Monsters and Synchro Monsters with the effect "This card cannot be Special Summoned except by Fusion/Synchro Summon" are also Nomi monsters. Examples include "Elemental Hero Mudballman" and "Trident Dragion", respectively.
Semi-NomiSemi-Nomi monsters are somewhat more flexible than Nomi monsters. They will have one of two phrases in their card text.
"This card cannot be Normal Summoned or Set. This card can only be Special Summoned...", and then the summoning requirements, for cards printed before Problem-
Solving Card Text.
"Cannot be Normal Summoned or Set. Must first be Special Summoned..." followed by a summoning condition, for cards printed after Problem-Solving Card Text.
Examples include "Fenrir" and "Dark Necrofear".
The difference between Nomi and Semi-Nomi monsters is that Semi-Nomi monsters can be summoned after they have left the field. However, this rule only applies when they are removed from play or sent to the graveyard. So, a Fenrir that has been properly special summoned can be special summoned from the Graveyard by "Monster Reborn" if it was destroyed by battle, or from the Banished Zone if banished by "Dimensional Prison". However, if it was returned to the deck by "Ehren, Lightsworn Monk", it cannot be special summoned by "Mother Grizzly".
All Ritual Monsters are Semi-Nomi. Fusion Monsters, Synchro Monsters, and Xyz Monsters are Semi-Nomi unless stated otherwise (see above).
Other Summoning RestrictionsCannot Normal Summon Or SetSome monsters cannot be Normal Summoned or Set, but have no restrictions on how they are special summoned. Examples include "Rare Metal Dragon" and "Wulf, Lightsworn Beast". The latter gives a method of special summoning, but it never says you must use that method. Thus, you could send either of the two monsters to the graveyard without summoning them, and then use "Monster Reborn" on either one.
Cannot Special SummonUnlike the other monsters covered, these must be Normal Summoned. Examples include all but one Spirit monster, some "Ancient Gear" monsters, and all "Wicked Gods".
Inherent Special Summon ConditionSome monsters, such as "Cyber Dragon" or "Gladiator Beast Gyzarus", can Special Summon themselves when certain conditions are met. These are conditions, not effects, and they do not start a chain.
Ignoring the Summoning ConditionsWhen a card says that a monster can be summoned ignoring the summoning conditions, it means precisely that: You can summon it without interference from any conditions. A perfect example is "Level Up!", which allows you to tribute a "Horus the Black Flame Dragon LV6" to special summon "Horus the Black Flame Dragon LV8", without having to destroy a monster by battle. Another example is "Ultimate Ancient Gear Golem".