I can already feel the blank stares of the people who haven't known me in one of my prior lens-wearing periods and haven't discussed these things with any of the fairly small number of other people out there who use them. So here's the background on what's going on.
There is a technique using rigid gas permeable ("hard") contact lenses known as orthokeratology. It's been around a long time, by which I mean my grandfather reports having used it when he was still an optometrist, although without having a name for it. When fitting RGP lenses you need to select a curvature for the lens so it fits the wearer's eye properly. With "Ortho-K", you select a lens which is intentionally very slightly too flat, but still fits well enough that it, well, fits. The nifty thing is that corneas are somewhat malleable. If you spend a year wearing a lens that's a tiny bit too flat, it will flatten out your cornea a little bit. The effect of this is that, if you're currently myopic ("nearsighted"), you become a little bit less myopic. Then you can get a new lens that's again a little bit flatter than the new shape of your cornea, and, as a bonus to getting well-corrected vision every day while your lenses are in, your uncorrected vision gets better over time (or, nifty, doesn't get as much worse if you're a teenager going through vision changes).
Sometime around the late-80s/early 90s, some smart people realized that if they designed lenses with the specific intent of doing this, they could get much better and faster results. The first of these was a non-spherical lens; take a normal lens (a slice of the surface of a sphere, IIRC), but make the bit in the middle have a significantly flatter curvature than the rest. This way you can get more flattening power than you used to, but still have enough of the right curvature for the lens to cling well to the eye (not fall out). With these, IIRC, you could change lenses every 2-3 months, and get more out of each lens.
The next step was an enhancement of that with a little ring-shaped well between the extra-flat part and the normally curved part. They'd reached the limit of how much they could push the cornea around, but found that if they made a little ridge of cornea outside the part of the eye you use for vision, they could use that as a place to deposit extra volume, so they could fix even more dramatic vision deficits, and have you changing lenses something like every 1-2 months.
Finally (for my knowledge and story), they came out with the lenses I now use, which use a related process called Precision Corneal Molding (PCM) or Corneal Refractive Therapy (CRT). They've significantly increased the customization of the lenses (I'm not sure if they're actually custom or just selected from a large array of options), and they do a more specific and tailored remolding of the cornea. They came up with an RGP lens that's safe to wear at night, and found that this meant you could make them a lot bigger (about the size of soft lenses; normal day-wear RGP lenses are tiny in comparison). They take digital images of your cornea with a camera and a weird black-and-white spiral getup to generate a surface map, and then they do some stuff I don't really understand and fit you for a lens, which arrives a few weeks later. This is typically the only lens you'll have to buy.
The normal process is that you put in the lens before you go to sleep (able to see perfectly, the lens still corrects your vision like any other RGP lens while it's in), and take it out when you wake up in the morning. With completely corrected, perfect vision. The very first morning. Over the course of that day, your vision will fade a bit, until by evening you may need to wear your old glasses again. The next day, the good vision lasts longer, and the fading is slower, and by day two or three you might not even feel the need to bother with your glasses. After that you're good: you wear lenses at night, you see all the time. Forget your lenses one night and your vision's a little blurry the next day, particularly in the evening. Forget two in a row and you might start having problems. But wear them again and you're good again. [Note: one of the cool things about all of these is that they're non-surgical, reversible procedures, so if something goes wrong you can just stop wearing the lenses and wait a while and you'll be back where you started. Obviously, that's also one of the minor drawbacks, you need to keep doing it.]
My correction is right on the cusp of the worst vision these things can actually correct to perfect vision during the day. My brother, who has worse vision than I, still needed either lenses or glasses during the day when he tried them. I think my corneas are also a bit more resilient than average. I go through the same process I just described, but it's kind of on a different scale. For the first few days, I go through a huge range of needed corrections over the course of the day, most of it in a range where I can't really function uncorrected, and big enough that with correction that's too weak it's still difficult to function. So it's a giant pain in the ass to get started, and creates the better part of a week in which I can't really effectively function as a professional programmer. But, hey, I'm unemployed right now, so that week will just be annoying, not career-affecting.
And that's why I can only sort of see while I write this.
In summary: they can do really cool things with rigid lenses to make your eyes work better even when the lenses are out, and you don't have to worry about them screwing up with a laser and making things both worse and uncorrectable. (They've probably improved that failure rate enough I should look into it again, but when it was new those numbers weren't making me happy.)