Cheese/Gvinas Akum
 
Gvinas akum is cheese which has been made by non-Jews and by rabbinical prohibition is only kosher if a Jew was present during the cheese making OR if a Jew put the rennet into the milk.
Note If a Jew owns the milk before processing, a non-Jew can add kosher rennet as long as it can be confirmed that the rennet is kosher, even if no Jew is present during the cheese making.
 
Origin of the Problem: Chazal were concerned that the rennet used to make cheese might be from a non-kosher animal or even from a kosher animal that had not been slaughtered properly. Shulchan aruch says that even cheese curdled by kosher plant enzymes (such as fig branch sap or substances from certain thistle plants) are subject to the takana.
Note Gvinas Akum is not related to chalav yisrael; they are separate halachot.

Note Even rennet-less cheeses need hashgacha (religious supervision), but some non-hard cheeses may be an exception. Ask a rabbi.