Cheese keeps changing after you buy it, so it needs to breathe without drying out. Plastic wrap pressed tight against the cheese traps moisture and can make it taste of plastic. Instead:
- Wrap it loosely in cheese paper, parchment or wax paper. You can put that in a loosely closed bag or container.
- Keep it in the vegetable drawer, where the temperature is steadier, and keep strong cheeses away from mild ones.
- Write the date on it so you know how long it's been open.
- Rewrap it in fresh paper every few days, or whenever you cut some.
How long it lasts depends on how much moisture it has. Once opened, fresh cheeses keep about a week, Brie and Camembert one to two weeks, semi-soft and semi-firm cheeses three to four weeks, and hard cheeses a month or more. How long does cheese last? has the details.
Found mold? On a hard cheese like cheddar, cut away at least an inch around and below the spot and keep the rest. On soft, fresh, shredded or sliced cheese, throw it out. See Can you cut the mold off cheese?
More on storage: All you ever wanted to know about cheese storage · Should cheese be kept in the fridge? · Can cheese be frozen? · How can you tell if cheese has gone bad?