There are many moulds that grow on cheeses, some fairly innocuous, others that are best avoided altogether.
Many soft cheeses commonly get a black mould. Any cheeses showing black mould should be thrown away.
The green moulds on hard cheeses like cheddar may not be so bad for you , but they send out long thin filaments, like roots, than can be invisible to the naked eye. To get rid of most of these means cutting off at least a good half-inch of cheese from the side where mould has started to appear.