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 made from hops so it does contain gluten.
2. At least traditionally, blue cheeses contained mold that was cultured on breadcrumbs, thus imbuing the cheese with gluten; however, because of modernization of manufacturing processes, it's not necessarily the case anymore. If you have celiacs disease, or have trouble digesting gluten, you'll want to also stay away from cheeses like Roquefort, Stilton, and even mold ripened cheeses like brie and Camembert, UNLESS, you are able to confirm that they were produced such that they do not contain or have acceptable amounts of gluten.
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.