Twisting the spine or stretching sideways

I would also like to know this.  They often feel really good.

That's a really good question! Both of these things (twisting and stretching to the side) can be healthy and safe, but it's important that your spine is tall and your discs are decompressed first.

Let's start with twisting. If your spine is shortened and you have bulging discs, and then you twist, the twisting can further compromise the discs. However, if you are lengthened vertically then your discs won't be damaged with a little twisting – it's in fact quite healthy in this case, and can be a great way (in the context of dancing, for example) to strengthen your obliques. Even when you have good baseline length, you want to engage your Inner Corset, using your deeper abdominal muscles to get a little taller, before you twist. 

Next, stretching over to the side. Similar thing – if you have bulging discs and then stretch over to one side without lengthening up as well, one side will get even more shortened and the discs even more squished. However, if you have a lot of vertical length, it's okay for one side to get a little bit shorter temporarily. As you stretch over to the side, you want to include lengthening / stretching upwards. Rather than just letting on side collapse as the other elongates, you want to reach up, and then you only need to reach over to one side slightly to give the other side a significant stretch. 

I hope this helps!

Monisha