I’ve been reading up a fair amount on yogurt whey since the SO and I started making our own two years ago.
Making yogurt is absurdly easy. Making Greek-style yogurt involves an additional step or two. The only difference between the two is the thickness. Greek yogurt is typically strained. The freshly made batch is poured into a strainer lined with cheesecloth. This allows the acid whey to drain out. The final product is then denser.
Here is the odd thing: whey (the Greek yogurt byproduct) is supposedly very healthy. It is sometimes used in health drinks and added to baked goods. As @snowberry points out though, there are several news articles out there now stating that, if added to the water system in vast amounts, it may be causing environmental damage.