In addition to gold and buildings, Creative Assembly has added another layer of depth to the campaign experience: population. Every province has a city and that city has a population. The units built in that province draw upon said population. The population pays taxes and also determines the level of the city. At each new level, buildings are unlocked which in turn permit better units and city improvements. It's actually quite possible to depopulate a civilization early in the game by engaging in a prolonged war with it. Sooner or later their cities will no longer have the population to build units.
There does come a certain point, usually at around 6000 population, where the natural growth rate of the city (usually at least 3%) will make up for almost any unit you can build, but there are other ways to eliminate the population. After being captured by siege, a city can be conquered (taken over but otherwise left alone), enslaved (half the population gets redistributed amongst your other cities) or sacked (the entire population is put to the sword). The latter two options also pillage the city for its valuables, and the last is great if you captured a town but are relatively certain you can't hold it and won't be able to claim it for a while, but want to deny the enemy a valuable resource.
It's generally best to leave important cities in the hands of family members, since this permits direct control. Otherwise, a city will default to auto-manage. While you can stop auto-manage from building units and buildings (which it's good at doing the latter, not so much the former), family governors also bring their special bonuses to bear. Not all your family members are destined to be generals, some are simply more skilled at ruling a province - they'll make building units cheaper, improve order and boost the economy.
For the most part though, it is best to leave your family members in charge of the legions. Not only do they have combat bonuses, they can gain experience and special abilities through combat. Their influence, command, traits and retinues will improve. We should note that traits are in general much more positive than in the previous two Total War titles - at least they are if you're as successful as we were with the Julii. Some of these traits are the typical character traits, some random and some based off player actions. Others are ranks from the Senate, like Quaestor, Praetor, Pontifex Maximus - each with benefits for holding the rank plus residual benefits if you've been promoted to another. Characters also gain retinue members. Defeated a barbarian army or city? There's a chance you may gain a Barbarian Turncloak, who will give further bonuses against Gauls, Germans, Britons and Rebels. Finally, a leader can gain custom titles like "Victor", "the Brave" or "Africanus". These depend on his actions on the battlefield, and we're guessing that there are less-flattering titles as well.
Diplomacy is exponentially better than previous games. For example, even trade is done through diplomats - they bargain for trade rights. Sometimes another civilization might want you to pay them in order for them to open up their ports. Negotiations are actual negotiations - if they offer something, you're free to counter-offer, and then they'll respond with an affirmative or their own counter-offer. These offers are broad too, provinces can be exchanged, tribute can be a one-time matter or every turn, trade rights, threats - all that and more. It's no longer merely a matter of "yes" or "go suck a lemon". Rome has introduced the give-and-take of diplomacy into the series.
Also, in what's sure to be a relief for all who've played those exhausting Medieval campaigns, the interface has been greatly streamlined. There have been too many changes to cover, but the one of biggest note should be that all completed construction comes down in one handy list, rather than an endless stream of pop-ups. Also, a handy family tree is provided to help you keep track of your sprawling dynasty.