>There are MANY MANY long threads already on this subject. A search would be very productive.
It's also a little tiring to discuss a subject that not a lot of people have a lot of knowledge of. But I've been thinking about the subject for a while, so here's a complete list of my knowledge of bivying:
-Bivying under a tarp is different from bivying under the stars (less exposure to dew, can get away with using a more breathable/less waterproof top fabric, not to mention you have a dry entry/exit in a rainstorm).
-Bivying under the stars is best in a desert environment, whether you're using a Gore-tex bivy or a water-resitant bivy.
-Sometimes the only purpose of a bivy (for instance under a tarp) is to keep the shell of your sleeping bag dry, but that can be a very important function if your sleeping bag is filled with down.
-In certain conditions, you are going to get wet at night, bottom line (camp in a river bottom, for instance, 100% relative humidity can permeate everything).
–In very moist conditions, sometimes the last thing you want is a wet piece of bivy fabric draping on your sleeping bag (this is where tent-style bivies might come in handy, if they're ventilated enough).
-In certain conditions, any bivy will stop being breathable (when the outside temperature dips below freezing and frost builds up on the the bivy fabric).
–If your bivy fabric is close enough (a snug-fitting bivy) to your sleeping bag, the idea is that the fabric itself will be too warm to frost up (what Andrew Skurka might describe as having the dew point outside of your bivy–that's the idea of a close-fitting bivy).
–If you know you will reach these conditions at night, however, you can stop your own perspiration from making the inside of the bivy (and potentially your insulation) excessively moist by using a vapor barrier.
On the other hand, there's a lot to be said for just using a breathable (mesh and nylon) "inner tent", to avoid a wet-out fabric coming in contact with your sleeping bag, and to allow ventilation if it begins to frost up, but then again, that would be a double wall tent, not a tarp and bivy.