The cheeses that should be kept in the fridge are those with a "bloomy-rinded" texture. These include Brie, Camembert, Roquefort and Swiss cheese. Semi-firm cheeses like Monterey Jack, cheddar and Swiss are also good to store in the fridge, as they will not become rock hard too quickly. Hard cheeses such as Parmesan, Romano and pecorino can be stored in the fridge for an extended period of time, but it is important to remember to remove them from the fridge before they melt.