The Quadratus Lumborum -- universally pronounced Kyoo-Ell -- runs from the back hip-bone to the bottom rib, on both sides, with connecting service to the sideways prongs of the lumbar vertebrae. Anglo-Saxons injure it a lot, because we generally hold our hips stiffly in line with our chests, and never give the poor QL a chance to completely contract or to really stretch. Belly-dancing would be impossible without the QL, as would climbing a ladder: any activity that hitches up one side of the pelvis up closer to the ribs requires that this muscle contract on the hitching side, and stretch on the other side.
Back when I used to "throw my back out" periodically -- before I learned the back exercises (really unattributed yoga, I learned later) that made those incredibly painful, disabling bouts a thing of the past -- it was the QL that I injured. So when I learned about it in massage school I was anxious to work with it.
But it was disappointing, at first. It was hard even to find it, especially on someone fleshy (like me). It's a back muscle, but it's mostly on the other side of the muscles, which at this point are pretty thick and powerful, right alongside the spine. If you try to get into it by pushing hard on the paraspinals, not much happens, because the paraspinals (being a cluster of mostly short-stranded muscles) hit their stretch limit before the QL's even started; and you can't squeeze it against anything, because there's nothing on the other side but intestines.
Well, that's one trouble with learning out of picture books: if you think of the muscle as a back muscle, then you only try to work it while someone's prone. You're stuck in two dimensions. There are a couple good ways to work the QL, but neither are from the back. Sidelying, you can bring the bottom thigh up (headwards) and nearly-straighten the top leg out to get a bit of a sideways stretch (you may need to tuck a towel or cushion under the side to make this work). then you can reach to the forward edge of the paraspinals and press nearly straight down: you've got the QL pinned against the spine, and you can really work it. Or -- this is my favorite -- with someone supine, you can reach underneath on both sides, and make fists of your hands, and simply roll their body back and forth over your fists. You can catch the edge of the QL with your thumb-knuckles and really stretch it. Their body weight does all the work. The intestines are free to get out of the way: they have all the room in the world. Most people are really grateful to get this kind of stretch -- similar to a toe-touching stretch, as far as the back muscles go, but a safe one. (I wince when I see people doing toe-touches, with a hundred pounds of torso or so pushing down on a three-foot lever; I'm always relieved when I see them come back up uninjured.) When you've done a number on the QL, you can finish off with a nice stretch -- with the person you're working with still prone -- by picking up both feet and pulling the whole lower half of the body, legs, pelvis, and all, to one side and then the other.
As Pamela Sundin-Hart, one of my favorite teachers at East-West, always insisted, "any muscle that attaches to the ribs is a breathing muscle." The QL has a crucial role in keeping the ribs stable so that when the diaphragm pulls, the rib cage doesn't simply fold in and follow it. When the QL is knotted up we favor it by breathing shallowly. Shallow breathing means less oxygen, and less oxygen means less energy: a jacked up QL will make you tired, and not just because you're in pain.