Challenging, deeply intricate, but hampered by some "hard-coded" restrictions that prevents a fully open-ended
One thing that doesn't seem to be mentioned that you wouldn't expect is that for military conquest, simply moving an army onto an enemy province will not give you that province. First you must maintain a siege and either break the city through deadly assaults or patient and sometimes lengthy sieges depending on different factors. Your war strategy can involve a blitz attack to try defeat your opponent's standing armies, leaving only small holding forces to maintain sieges, or you can attack with slow moving front, capturing cities as you get to them. Attrition (representing men dying from the weather, disease, or lack of food) can in many cases be your worst enemy (or your best friend, when it helps defeat an enemy). After successfully occupying the territory, you will only own the province after you negotiate a peace deal with your enemy that involves them ceding the province to you. The fact that you occupy the province makes it possible to to include it in a peace deal, as well as giving you better bargaining power in negotiations.
My main gripe with this game is that some of it is "hard-coded" so-to-speak, in a way that penalizes some actions which should not be penalized. I believe it is this way in order to maintain relative balance between small nations and large nations, but for those who understand how the game works, it can force you to make some strange decisions.
For example, the cost of investments in technology in order to advance a level are at least partially governed by the number of provinces you own. But the value of the provinces does not seem to be taken into consideration. So gaining a low-value province can hurt your technology costs as well as your stability costs (especially if the province is of a different religion and culture of your own). So you may be better off taking only the most valuable provinces, and avoiding the low value provinces even if they would be easy to gain. Of course, it would be extremely unbalanced if the large nations paid as much to advance levels as the small nations, but I think the game should at least consider the value of the province in determining your investment costs.
Another example is your reputation, or "badboy" points. Badboy points are gained through aggressive and threatening actions. You gain Badboy for declaring war and taking provinces in peace agreements (less if you were the defender who was attacked in a war). You don't want badboy points, as it can make you a target of nations. There seems to be a trigger point where if your reputation gets bad enough, many nations all declare war at once. Over time, your reputation improves. But one thing that stands out as a major reputation hit is annexing a nation. So basically, you can take many provinces of a nation and your reputation won't suffer too much. But take that last province, destroying the nation, and your reputation takes a large hit. So you generally will just want to make that last single province into a vassal, and only ever take that province after some other country has annexed it themselves. Sure, this is a work-around, but it does feel a bit unnatural.
Yet another example is that you get less tax income from provinces if they do not have a contiguous land connection of your own provinces to your capital. This means that if your capital is an island province, you'll have this penalty on every other province you own. For the continental nations, having a connection to your other provinces already has a benefit in that you can better defend all parts of your land without needing separate armies, so I see no reason why it needs further encouragement. Though this may not be too big of a deal in the grand scheme of things and the idea behind it is understandable, it seems like an unfair penalty to some nations. Perhaps a better solution would have been some sort of penalty based on distance of the province away from your capital, rather than land connection.
Some more examples of this "hard-coded" feeling are:
Pagan religions such as Native Americans have such a steep technology penalty that playing as a pagan country may not be worth it. Of course, these nations are meant to be "minor" and to be conquer easily by colonial nations, but it seems to be an unnecessarily severe penalty. In addition, the "tribal" governments can never advance to a more advanced government type unless you edit the game's scripts. Alliances are somehow limited. You can only have about 3 or 4 of them. Some nations can be very friendly towards you and would benefit from being allied with you, but you still won't be able to get an alliance. It would have been best if nations only determined if they would ally with you based on whether it would help them or not (and whether they could trust you to honor the alliance according to your relationship). Some more "teaming up" against the strong guys would have been a nice addition too.
So that said, the game is still fun and challenging. And if you play as the European nations, you won't really be concerned with any of these "hard-coded" issues. The game is made to be played with European nations, and other nations seem to be there for a diversion and for completeness. It's still very interesting to see how each game you play causes the regions and powers of the world to develop quite differently because of your influence. Every game you play, you'll probably learn something new about the game, or you'll learn a better strategy for the next game. There's also some mods you can download to change the game for a new experience. Some mods change the game and it's rules completely, while others just add a few touches. So if you're the type who really likes a complicated and nuanced game, you'll probably like this.