NOTE: This content is not intended to provide medical advice, which should be obtained directly from a physician.

The short answer is that most cheeses that you will buy in the grocery store are gluten free. You will want to check ingredients before you eat anything new to make sure that the cheese does not contain gluten products, but, if you are unable to eat gluten for whatever reason, you should get excited about the possibility of eating cheese, with the following caveats:

1. Flavored cheeses may have food items with gluten introduced to them. One example, is beer-washed cheese. Beer is typically brewed with barley or wheat, which contain gluten, so beer-washed cheeses can contain it too.
2. At least traditionally, blue cheeses contained mold that was cultured on bread, which could introduce gluten. Many producers now use lab-grown cultures, and some testing of commercial blue cheeses has found very low levels, but it varies by producer. If you have celiac disease or trouble digesting gluten, it's worth checking with the producer (or your cheesemonger) about cheeses like Roquefort and Stilton, especially artisan ones. Mold-ripened cheeses like brie and Camembert are generally considered gluten free too, but as with anything, check the label.
3. Shredded cheeses that you might buy in the supermarket are often powdered with cellulose so that it does not clump together. Before you buy shredded cheeses, you will want to check the label-- OR, you can buy and shred your own cheese!

Once again, before trying any new foods, you'll want to make sure that you read a label. If you are buying cheese from a cheese shop or counter at a grocery store, the cheesemonger is usually very knowledgeable and can can answer any questions you might have.