What does culture do?

That means the enemy planet is losing allegiance, and unless your opponent pushes your culture back (either by his, or blowing up your culture centers), after a while the planet will rebel and turn neutral.

Each race also gets various bonuses while being under the influence of their own culture. Advent get extra shield mitigation, for example, or Vasari get extra damage.

On top of that, culture raises your own planets' allegiance, which means they make more money and resources for you.

Your culture will in that case be decreasing the enemy's allegiance. That means he gets less income from taxes and resources there, and if his allegiance goes too low, the planet will rebel.

Yeah, don't ignore culture. I forgot about it completely in one of my early games, and before I knew it, my capital was down to 60% allegiance and dropping fast.

Tangent question:

A friend of mine told me that you can't colonize worlds inside someone else's culture. Is that true? If so, can I use culture as area-denial, by flooding my enemy's space with my culture and then destroying his colonies?

Yes you can.
The enemy can't capture planets if you have strong culture over it.

Yep (if your culture is strong enough).

Yes. Exactly.

You can't conquer the universe with propaganda... but you can make it a very nasty rebellious place!

Awesome. What constitutes "strong enough"? Is there any quantitative measurement of the amount of culture in any given point of space? I really, really love the look of the phase lines turning your faction's color, but I don't know how to translate that into "strong" culture. Any suggestions?

Check out your planets' infocards. If they're spreading culture, the exact amount will show. While you can't see how much your enemy spreads, if your line is moving forward, you're winning. If it's moving back, the enemy is winning. Sometimes your line will stop at a planet, and theirs will also - then you can select the planet, and to the right of its picture on the bottom, the middle box is for allegiance - hover over it and see if it's changing in your favor or the enemy's.

Capital ships also have an impact on culture. If you have a capital ship parked above a planet said planet will lose allegiance slower.

Alternatively, parking capitals at neutral planets will make hostile culture poof from them also!