I was trying to remember when Viparita Karani, colloquially known as legs-up-the-wall, first burst onto the scene. It’s not a pose that is included in the more than 200 poses of BKS Iyengar’s Light on Yoga. I suspect that Gita Iyengar had a lot to do with propagating it.
I first came across the delightful variations of the pose that I call the Viparita Karani cycle – Legs straight up, legs in Supta Konasana, legs in Baddha Konasana, and legs in cross-legged – in  The Woman’s Book of Yoga and Health by Linda Sparrowe and Patricia Walden.
Here’s Heather in one of these variations with her YogaAnywhere card nearby:

Viparita Karani is a favourite with so many people because it will sort you out. If your lower back is a little sore – maybe you didn’t even know it – after 5 or 10 minutes in this inversion, it will have eased. If your kidneys are somewhat achey, the pose will soothe them. If you have just done an energetic practice and your energy is slightly wiry, Viparita Karani will get it back on an even keel. (The pose is recommended to ultra athletes to rest their legs after strenuous exertion.) But, your energy is badly depleted, a long timing in the pose will revivify.
What’s not to love?
I know from experience that yoga teachers are notorious at self-care. Often we teach too much and don’t practice enough, always looking after others. At different times in my life, Viparita Karani has been a life saver and even got me back on track to take better care of myself.
Here’s a set-up that I use occasionally if I want to make the pose even more inverted.

On the other hand, if you want a less inverted pose, after you lie down, rest your lower legs on the seat of a chair. For complete comfort, cover your eyes with an eye pillow or soft cloth and place a bolster over your legs. Don’t worry if you drift off into one of those Savasana states, you will resurface peaceful and renewed.