How can switching religion or civics be useful?

I don't really understand why you're able to change an entire civ's religion through espionage.  How does that happen?  The spy breaks into the national church and puts up your holy relics, and no one notices?  This is especially weird since you can change the entire civ's state religion in just one city.  Can someone please tell me any time in history where an entire civilization's religion changed because of a spy?  It would be much better if he could just spread your state religion in the city he was in.  Kind of a substitute to missionaries when you don't have an open borders agreement.  Not quite as fun, though.

Oh THAT! is how that works!?! Wow. Didn't realize it changed the religion or civics for the entire society!  That _is_ powerful then.

I get the use of the "Foment  Revolt" for 1 turn, it creates civil unrest in the city that keeps the mlitary there busy = lost fortification for one turn.

What I don't quite understand is how the "Cause Unhappiness" (or whatever it is labeled) differs from this? Since this lasts longer (8 turns evidently in a Marathon speed game) I guess it is supposed to be a more chronic social upheaval, but I'm not clear how to best make use of it. So far, I've mainly used Poisoning Water, and Stealing Techs. The espionage part of the game really does add a lot to it.

Perhaps it is by influencing the person or people on top.  Get close with them and convince them to change the state religion.  Kind of like the influence that Rasputin had on Nicholas the 2nd.  Not that he was a spy, but you get the idea.

I tend to play on huge maps lately, and the AI seems to do it's best to not follow my religion. This probably makes certain things (like the Apostic Palace), but more to the point, it causes me to have to engage in counter-aggression against crummy AIs that seem to hate my civ because of the religion choice, even though I've flooded their cities with it.

Forcing religious changes would probably be the single greatest thing to improve my style of gameplay. I really look forward to learning how to do it.

If I understand it correctly, it adds 8 unhappy to the city, depending on the time and point in the game, that might not actually be enough to stop the city from working, but if it is, then in that way it's more effective than formenting revolt. Again, that's if I understand it correctly.

Truth be told, I am a bit of an emotional player sometimes, and I find my spies really only come out when the AI has aggravated me through some callous and unneccessary act of aggression. In which case, I have a cruel tendency to go into the city and simultaneously "Cause Unhappiness" and "Poison Water Supply". Then, there's 8 less city workers/population bringing in food, and food resources for 8 more citizens being consumed. (If I understand correctly.) The city starves rediculously fast. I do this in their capital, espeically if it's at about 6 or 7 population at the time, and if the capital is too far away for me to reach, or really want to take with my forces. Capitals are often great producers of things, and usually quite populous compared to other cities, if I can lay them to near waste, I feel I'm really helping compromise my opponents economy.

I'm sure if I did that even once in a multiplayer game, my friends would never forgive me. In truth, it's quite uncool, if you think about it. ;-)

True. And remember, a lot of "Great Spies" who appear, aren't at all spies historically. Some are just well-learned and admired people in history, or developers of lingusitic systems (that would later be cryptographic ones). Not all spies need to be cloak-and-dagger Atomic Bomb thieves, some can and should be diplomats. I always think of spies as the replacement of diplomats that they had in earlier versions of Civ.

p.s. Apologies to all if I'm not using the quote feature well. I'm actually not very used to participating in online forums.