Most special summons stem from the resolution of an effect on the chain, but there is a small group of monsters that are special summoned without the use of activated effects. The special summons work a lot like normal summons, because you can usually only perform them during the main phase of your own turn. You don’t "activate" an effect when you special summon these monsters, so they don’t start a chain.

These monsters are thought of as having an "inherent" special summon ability. They aren’t special summoned by another card’s effect and they aren’t special summoned because something has happened to them. They are special summoned during your main phase, like a normal summon, either when specific field conditions are met or by paying some kind of cost.

from Metal Raiders was the first monster to use this type of special summon. When you special summoned Gate Guardian (not an easy task), you tributed all three of the required monsters from your side and then placed Gate Guardian onto the field. You never "activated" an effect when you did this, so a chain wasn’t started. It was more similar to a tribute summon than it was to something like Monster Reborn. Other special summon effects we had at the time (Elegant Egotist, Monster Reborn, The Flute of Summoning Dragon, etc.) would "activate" and start a chain.

Pharaoh’s Servant gave us The Fiend Megacyber, a monster that could be special summoned if the conditions on the field met specific requirements, with no cost to be paid. Cyber Dragon, Grandmaster of the Six Samurai, Great Shogun Shien, Rainbow Dragon, and Elemental Hero Bubbleman all have this kind of effect. You can special summon them free of charge as long as the field meets specific requirements demanded by the monster you intend to special summon.

Labyrinth of Nightmare brought monsters like Dark Necrofear that could be special summoned simply by removing specific types of cards in your graveyard from play. Removing cards in your graveyard was similar to tributing monsters on the field, and the special summon would not start a chain. Fast forward to the present and you’ll see many monsters that have this special kind of quirk. Spell Striker, Dark Armed Dragon, Frost and Flame Dragon, Gigantes, Dark Rainbow Dragon, and Fenrir are all special summoned with similar methods.  

The cards removed from play are not "targeted," so it isn’t possible to chain an effect that will remove them from the graveyard and think that this will somehow stop the summon. The cards are removed from play and the monster is special summoned onto the field, with no chance in between to interrupt the action. Like tributing monsters for a tribute summon, you don’t get your cards back if your opponent negates the special summon and you can’t interrupt the process by activating effects.

We also have Fusion monsters that do not use the chain when they are special summoned. The "Neos" monsters, known for "contact Fusion" on Yu-Gi-Oh! GX, don’t start a chain when they are special summoned from the Fusion deck. You return the required monsters to your deck and immediately place the "Neos" Fusion monster into play. The various "VWXYZ" Fusion monsters and the "Gladiator Beast" Fusion monsters also share this property.

Horn of Heaven and Black Horn of Heaven can only negate the special summon of monsters when they are special summoned through their "inherent" special summon effect. Solemn Judgment is held back in the same way, but it can at least negate spell and trap cards that are often responsible for the special summon of monsters. Solemn Judgment cannot do anything to stop a monster that is special summoned with another monster’s effect because it cannot negate the effects of monster cards.

Royal Oppression is a bit more flexible. It has the ability to negate both "inherent" special summons and special summons generated by the activated effects. Unlike the previous cards, Royal Oppression is a continuous trap card and must already be face up on the field before the monster is special summoned. When your opponent activates Monster Reborn and your Royal Oppression is face down, you can activate it by flipping it face up, but you will not be able to use its effect in the same chain. Royal Oppression makes things interesting this way.

You also have to keep it out of the damage step. Counter-trap cards can be activated in the damage step, but Royal Oppression cannot. You will find that Divine Wrath will be your only consistent means of negating special summons in the damage step, because it can negate the effect of the monster that intends to special summon another monster to the field. It is rare for a spell or trap card to special summon a monster in the damage step. Cards intended for use in the damage step—like Hero Signal and Damage = Reptile—are uncommon.