Ok, I have read some posts about the AI and have played other games like this with bonuses which make sense to me, but what happened to me this last game infuriated me so much at the blatant AI cheating that I had to post about it. 

The AI was about to enter the last era and I was watching them closely because I was 1 star away myself when they finally enter into it the message pops up "A player has entered the last era, if any of these things occur the game ends, yada yada". Anyway I was expecting that and closed that popup just to receive the message "The (pink) player has constructed a space station" and its corresponding messages...

Now how in the world does that happen if the AI isn't cheating? the space station is like 5 technologies into the next era, not to mention having to actually construct it in one turn. I like challenging games but this isn't challenging... this is cheating which just left a really sour taste in my mouth... on that note though I also think the tech is researched too quickly in later eras.

Hi, could you send us a save so we can have a look at what the AI is doing ? She shouldn't cheat this much ^^

auto-save 1798.ctr

Here's the one closer to when I ended it all.

Something similar happened to me.  Although I was the first to Contemporary, the second (who, indeed, had been French) followed some time later, and within a few more turns I got the Space Station cutscene for them.

It was funny, because her armies were still running around with swords...

After the game ended (I won easily, since my economy dwarfed the rest of the planet) on the post-game stat screens, it was clear that the AI player was way ahead on tech going into the Contemporary.

I don't think any cheating was required.