Many – if not most – hard cheeses are made using a substance called rennet. Rennet is a nice word for “scrapings of the inside of baby cow stomachs”. And while it is used for a functional purpose (to get the cheese to coagulate); it remains in the finished product.
Rennet (also called chymosin) is used especially in the production of parmesan cheese and higher-quality name brand cheeses. No-name brand cheese usually use microbial enzyme, meaning the coagulant is derived from bacterial sources rather than dead cow.
Even though a majority of cheese manufacturers still use a rennet-based process, there may soon be another alternative: safflower rennet, developed by an Argentine company call SemBioSys. Presumably, the enzyme will be bioengineered (genetically modified), but could be less expensive to use.
Rennet can also be produced by fungal fermentation.