Cheese is made from milk (often cow's, goat's or sheep's) that is allowed to thicken due to bacteria (naturally occuring or added), until it separates into liquid (whey) and semisolids (curd). The whey is drained and the curds are pressed into shapes; this is fresh or unripened cheese (varieties include cottage cheese, cream cheese, ricotta, etc.). The other general type of cheese is ripened or aged cheese, in which the curd is then cured by a variety of processes including heat, bacteria, soaking, with the addition of herbs, spices, and in the case of most cheddars, added dyes. After curing, the cheese is stored and aged. Ripened cheeses are further classified by texture or process: Hard (Parmesan), Semifirm (cheddar), Semisoft (gouda), Soft-ripened (brie), Blue-veined (blue), pasta filata or spun (mozzarella). The reduced-fat cheese are made from reduced fat milk and additives, and these cheeses have less flavor and do not melt well as a result.
Fresh and soft-ripened cheese should be wrapped tightly and stored in the coldest part of the refrigerator for no more than 2 weeks. Other cheese should be wrapped in waxed paper and kept in the warmer part of the fridge (they are still living so let them breath), and if mold develops simply cut it away.
The colder cheese is the easier it is to grate, but all cheese will taste better if brought to room temperature first.