Store cheese in the produce or dairy compartment of your refrigerator. It will continue to age. Cheese should be wrapped airtight in plastic or aluminum foil; change the wrap every time you use it. Roquefort cheese will benefit from being wrapped in a damp cloth. It will stay fresh for months if rewrapped each time a piece is cut away.
The molds that form on natural cheeses are unappealing but harmless. If the mold is just on the surface, scrape it off with a small knife. Moisture is what causes the mold to form. Cheeses that tend to mold quickly should be wrapped somewhat loosely in foil, which allows the cheese to breathe and the moisture to escape.