Good news: they're harmless, and they usually mean the cheese has been aged well. There are two kinds, and neither is mold.

• Tyrosine crystals. As a cheese ages, its proteins break down into amino acids, and tyrosine is one that doesn't dissolve easily, so it clusters into tiny hard crystals. You'll find them inside long-aged hard cheeses like Parmigiano Reggiano, aged Gouda and Pecorino Romano. They're the satisfying crunch.
• Calcium lactate crystals. These form when lactic acid and calcium from the milk combine. They're most often seen as white specks or a crust on the surface of aged cheddar. They have a softer, slightly grainy crunch and a neutral taste.

Some people call them "flavor crystals," though the flavor really comes from the long aging that produced them. Seeing them is generally a good sign.

How to tell crystals from mold: crystals are hard, crunchy and small, and they're scattered through the cheese or sitting as a dry powder on the surface. Mold is fuzzy, slimy or colored (green, blue, black or pink). If you're not sure, see How can you tell if cheese has gone bad?

Related: How can you tell if cheese has gone bad? · Can you cut the mold off cheese? · How long does cheese last?