I always have this question. Big chefs said cheeses are alive, they need to breathe. Cheese makers said cheeses can be kept for at least 2 months wrapped with either wax paper or a tochon/dish towel. Other cheese sellers sell their cheese in a sealed wrap (for hard cheese).
I tried the following ways:
Cheese in fridge in paper or tochon, they tend to make other food smells cheesy or absorb the smells of other food. Other food get mouldy easily. It will be ideal if you have a fridge just for cheese.
Cheese in sous vide vacuum sealed bags. Well hard cheese like Parmesan works, sous vide cheese for a long time is too dry, the taste changed.
It’s mostly how I kept my cheese, in an airtight glass box with a plastic lid. Pro: the fridge doesn’t smell cheese. Con: cheese sweats a bit.
How do you store your cheese?