While we haven't gotten anything super-detailed about how each city-state is run, we can look to their Grand Companies for a basic idea.
We know that Ishgard had been under rule by their church for the past 1000 years, but how Heavensward and 3.1 (at this time of writing) will effect that is still to be seen.
Likewise, we know that Ala Mhigo formerly had a king, but fell to Garlean rule. We don't know much of Othard and Doma, but we know that Garlean conquest was successful, and for a number of yers, there was peace. The Domans rose up when they believed Garlean rule to be a weaker point, due to the War of Succession, and the Garleans razed their lands, which is why we have a bunch of Doman and Auri refugees in Eorzea.
We know that Ishgard had been under rule by their church for the past 1000 years, but how Heavensward and 3.1 (at this time of writing) will effect that is still to be seen.
Likewise, we know that Ala Mhigo formerly had a king, but fell to Garlean rule. We don't know much of Othard and Doma, but we know that Garlean conquest was successful, and for a number of yers, there was peace. The Domans rose up when they believed Garlean rule to be a weaker point, due to the War of Succession, and the Garleans razed their lands, which is why we have a bunch of Doman and Auri refugees in Eorzea.