The Yonko are one of the biggest forces in the world of One Piece and they rule the New World like Kings. Their influence is such that if they declare a territory as theirs, no force in the world can oppose their decision.
On the other hand, the World Government actively opposes the influence of the Yonko, now more than ever. Most countries in the world of One Piece are allied with the World Government and seek protection from them against pirates.
10 Yonko: Fishman Island
Fishman Island lies 10,000 meters under the sea right below Mariejois. If someone has to reach the New World, passing through Fishman Island is necessary. Often, the place was subjected to barbarism by the pirates until Edward Newgate declared the island as his.
After Whitebeard's death, Charlotte Linlin of the Four Emperors decided to declare it as her territory. Currently, the island is under the protection of the Straw Hat Pirates.
9 World Government: Alabasta
Alabasta is quite a beautiful kingdom located in the Grand Line. It is led by the Nefeltari family, and its current ruler is Nefeltari Cobra. Although originally part of the 20 Kings, Cobra's ancestors decided to live in the surface instead of Mariejois.
Nonetheless, they are still allied with the World Government and seek protection from them, at least for now.
8 Yonko: Wano Country
Wano Country is located in the New World and is currently being focused on in the story. The place is completely isolated, thanks to the Kozuki Clan's orders centuries ago, therefore no outside power can interfere with their country.
Once Orochi came into power, however, an alliance with Kaido of the Four Emperors was formed and the place has been ruled partly by him since then. To open up Wano Country, the Straw Hat Pirates will have to go through the Beasts Pirates and take down Kaido.
7 World Government: Dressrosa
Another country in the New World, Dressrosa is ruled by the Riku Family right now, however, upon its formation, the place was ruled by none other than ten Donquixote Family.
Like most others of the 20 Kingdoms, the Donquixote Family went on to live at Mariejois, which led to the subsequent rise of the Riku Family. Ever since the old times, Dressrosa has always been protected by the World Government.
6 Yonko: Totland
Totland is one of the few countries to have actually been created by a Yonko. This place is the creation of none other than Charlotte Linlin, one of the Four Emperors of the Sea.
Totland consists of 36 islands, each of which is ruled by a Minister-in-charge. The main island, called Whole Cake Island, is ruled by the Queen of Totland, Big Mom herself. Their forces are extremely powerful and not even the Government can mess with them.
5 World Government: Goa Kingdom
Goa Kingdom is a country filled with nobles, somewhere in the East Blue. Monkey D. Luffy and his brothers spent quite a lot of time in this country during their childhood.
Goa Kingdom is led by King Stelly, Sabo's adoptive brother. Their influence as one of the 20 Kingdoms ensures that they always get protection by the World Government. Thanks to them, pirates usually choose to stay away from this country.
4 Yonko: Beehive Island
Beehive Island is one of the most significant places for piracy in the world of One Piece. This place is known to have been the origin of Davy Back fights and was also where the Rocks Pirates crew was originally formed.
Apart from its significance, the place is known to be Pirates' Paradise because it isn't lacking in anything that their kind adores. Currently, it is under the control of none other than Marshall D. Teach, also known as Blackbeard.
3 World Government: Sakura Kingdom
Formerly known as Drum Kingdom, the Sakura Kingdom lies in the Grand Line and is currently ruled by Dalton. Formerly, the place was under the control of the cruel King Wapol, who was eventually kicked out of the country, thanks to help from the Straw Hat Pirates.
Sakura Kingdom was able to take part in the Reverie, which implies that they're quite an influential country, even more so after the Wapol's banishment from the country.
2 Yonko: Sphinx Island
Said to be a poor place, Sphinx island was the home of Edward Newgate, aka Whitebeard. During his time as one of the Four Emperors, Whitebeard was the one who sent supplies to this island every month to ensure their safety.
However, after his death, it is unknown who exactly protects this island. From what the story seems to imply, Marco the Phoenix is the only person-in-charge of protecting the place all by himself.
1 World Government: Prodence
The Kingdom of Prodence isn't seen enough in One Piece, however, we do know that it is located in the New World. Led by Elizabello II, Prodence is known to be a close ally of Dressrosa.
Like almost every other country from the 20 Kingdoms, they attended the Reverie and discussed the problems of the world with the Government. They also played a hand in the abolition of the Shichibukai system.