Hi everybody!
In the interest of educating folks who may not know a whole lot about gluten-free pizza, I figured I'd put together this FAQ; hopefully it'll wind up being helpful to someone. If anyone has anything they want to add, I'll be happy to edit this post accordingly
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What is gluten-free (GF) pizza?
Gluten-free pizza is made using flours and other ingredients that do not contain gluten.
What is gluten?
Gluten is a protein found primarily in wheat, barley, rye, spelt, and other wheat-related flours. It is the main ingredient that allows normal dough to trap yeast-produced fermented gases, due to the strength it gives the internal "cell structures" of the dough. Flours that do not contain gluten include corn flour, bean flour, tapioca flour, and rice flour, along with a few others.
How does gluten-free pizza differ from normal pizza?
Because there is no gluten in a GF pizza, the dough is much harder to prepare. It is softer, more fragile, and cannot withstand normal yeast fermentation without the aid of ingredients that act as protein substitutes (such as eggs, xanthan gum, and others). In fact, because of its lack of strength, gluten-free dough often is forced to exist as more of a batter than as a solid ball of dough.
Also, since no single gluten-free flour can be directly substituted for standard wheat flour (due to taste), a variety of gluten-free flours are usually employed in a blend. Given these limitations, it is incredibly difficult (most people would say "impossible") to make a GF pizza whose taste and texture mimics that of a regular pizza. Instead, the challenge is to get as close as possible

GF pizza also tends to be much more expensive than normal pizza, because gluten-free ingredients tend to be more expensive in general.
In that case, why would anyone want to eat gluten-free pizza?
Generally, there are two groups of people who eat gluten-free pizza: people who don't WANT to eat foods containing gluten (because they believe it to be unhealthy), and people who CAN'T eat foods containing gluten (because they have celiac disease).
What is celiac disease?
Celiac disease is an auto-immune condition that affects approximately 1 in 133 North Americans. For people with celiac disease, gluten causes physical damage to the small digestive villi that line the small intestine. This damage, over time, usually leads to malabsorption of nutrients, gastrointestinal distress, and weight loss. Even more serious are the long-term effects of intestinal exposure to gluten; celiacs who continue to consume gluten run extraordinarily high risks of non-operable lymphoma and other lethal auto-immune diseases.
Celiac disease is not merely an "allergy"; it also is not a condition where "some gluten is okay, as long as you don't eat too much." There is no cure for celiac disease, and the only treatment is complete abstinence from ALL gluten--for life.
What are some other considerations when making gluten free pizzas?
The challenges of making pizza without gluten are myriad. The dough itself presents the first problem, as described above. There are also issues regarding other ingredients and toppings; for celiacs, it's important not only that those be gluten-free, but also that they are prepared "in isolation" so as to avoid cross-contamination with foods that contain gluten. This can be very difficult when trying to prepare gluten-free pizza in a house or social situation where non-celiacs are present.
Even ingredients that are normally gluten-free may be unsafe. For instance, some flour mills may produce rice flour (which is normally gluten free) for sale in stores....while making wheat flour in the same mill, on the same production line. That rice flour would be unsafe for celiacs.
There is also a question of prep equipment. Pans and utensils used must be dedicated to gluten-free use only, to avoid cross-contamination with gluten.
Gluten free dough also tends to be more "batter-y" rather than a solid dough, due to the lack of gluten (many GF pizzas are almost "poured" out onto pans rather than being rolled out). Thus, GF pizzas often have to be par-baked without any toppings to firm up the crust.