The grains that contain gluten that Celiacs must avoid are:

• Wheat
• Barley
• Rye
• Triticale

Oats are also on the possibly-exclude list; studies on them as a gluten source are incomplete, but better safe than sorry.

Beer, of course, is primarily made with barley (and often wheat), so brewers of gluten-free beer need to resort to other gluten-free grains as their main source of fermentables. The primary ones are:

• Sorghum
• Buckwheat
• Maize (corn)
• Rice
• Millet

Most of the gluten-free beers I’ve seen use sorghum as their base grain source, and are often supplemented with buckwheat and rice. Deschutes Brewery, for instance, brews their Gluten-Free Golden Ale with sorghum, brown rice, and roasted chestnuts (more on that one later in the week).

Honey, fruits, and nuts are also all gluten-free, of course.

In addition to the list above, there are many other ingredients (sources of starches/fermentables, basically) available that could be very interesting when used in a beer:

• Quinoa
• Amaranth
• Chickpeas
• Tapioca
• Arrowroot
• Yam/sweet potato
• Lupine (domesticated)
• Montina (milled Indian rice grass)

Whether any of these “secondary” ingredients make it into a commercial beer remains to be seen. (If you’re homebrewing your own gluten-free beer, then the sky’s the limit, of course; for the most part, you will need to be set up for all-grain brewing to mash the grains yourself—although lately I have seen sorghum extract syrup available to extract brewers at my local homebrew shop.)

Good further sources:

• Wikipedia
• Celiac.com
• The Vegetarian Society