I understand how the gluten in wheat flour works to capture the gas formed by either yeast or baking powder or soda, but what makes the non gluten containing flours rise?
In normal baking, the proteins glutenin and gliadin in flour bond with the water and with each other to form long strands and sheets of what we know as gluten. Many baked goods rely on the formation of gluten to trap gases released by leavening agents in order to make the product rise. The most common example is the gluten formed in making bread, although gluten is found in lesser amounts in biscuits, cakes and cookies, as well.
Gluten sensitivity is a reaction to the gluten found in most baked goods. The proteins that make up gluten can be found not just in wheat, but also barley, rye, triticale and some other grains. Others, like oats, may be contaminated during handling and processing. Gluten sensitivity affects the body's ability to absorb nutrients.
Many gluten-free baked goods can be bought, or made at home. Flour made from rice, corn, beans or other starchy foods is used to provide the substance of the product, and yeast or baking soda or powder are still used to provide the lift, but because these flours don't form gluten, something else is needed to trap the gases produced by the leavener. The two most commonly used ingredients are egg and xanthan gum, both of which allow the gases to be held until the starches can set enough to hold the volume.
Because bread made in this way lacks the long protein structures of gluten, its consistency is somewhat more cake-like than regular bread. All gluten-free products will tend to be denser and more crumbly that their gluten containing counterparts.