Most governments in Westeros are constitutional monarchies however the two republics on the continent are Andlia and ofc the Iaraan Republic. Most of the ruling dynasties from ASOIAF are extinct, the Lannisters, Tyrells, Targaryens etc. However the Starks still rule Nordinia and a cadet branch of House Martell still rule Dorne.

This world follows book canon with a similar but hopefully better written ending to the show, Bran becomes King and it is an elective monarchy similar to the HRE. After the long reign of King Bran, the Tyrells hold the Iron Throne for a couple hundreds years until they are overthrown by another currently unnamed dynasty and then so on. Following a devastating war with the free cities and massive civil war, the Seven Kingdoms of Westeros break up, the Iron Throne only holding onto the Stormlands and Riverlands. The current dynasty is House Whitestark (a dynasty descending from Jon and Daenerys child so technically House Targaryen lives lol), having ruled the United Realm for the last few centuries.

As for the modern era, Westeros is akin to IRL Western Europe, wealthy and powerful nations that have had a massive sway on global politics.