Cities level up as the population of the city grows. With each level, a percentage increase to the city's gildar, arcane research, or worldly research production is possible. Each city has a population cap on it based on the amount of housing constructed in the city as well as natural improvements such as refugee camps. To build housing, food is needed, which can be obtained through Sovereign abilities, resource improvement (farms, apiaries, etc.), and through spells. Additionally, population generates gildar through taxation. The higher your population, the more gildar a city will produce.
Construction of buildings is limited by resources, population, and the city level. Cities no longer have a building limit based on tiles, but rather based on the civilization's population. A limited number of buildings can be constructed to produce material, arcane knowledge, and worldly knowledge due to the population required for each building and a gildar tax. As such, it is a good idea to specialize cities based on nearby resources, only constructing buildings in that city that complement the nearby natural resources as well as matching the level up bonuses to the resources produced there.
Each city creates an influence area around it. Natural resources inside this influence area can be built on (when the appropriate technology is researched and material is available) to provide a greater boost to resources for that city. New buildings must be constructed on tiles adjacent to already finished buildings, except for natural resource improvements. If a natural resource improvement isn't attached to the buildings in the city, then it can be destroyed by your enemies (including wild units such as bandits and spiders). However, if attached to a city, the natural resource improvement cannot be destroyed. When attached to a city, attacking a natural resource improvement is the same as attacking the city.
When an enemy unit moves into a tile containing your city, the enemy unit will attack the city. If no units are stationed there, the city will automatically be captured. If you have units stationed in the city, a battle will ensue. Being stationed in a city grants a HP bonus to units, in addition to providing defense bonuses if certain improvements are built. If you when the battle, the city remains yours, and if you lose then the city is conquered by the attacking unit.
Finally, cities have item shops for heroes. Your cities and foreign major faction cities have equipment that is available to them through research, while neutral cities will sometimes sell special items from before the cataclysm.