One effect that creates problems for some people is that these are lenses, and they don't just move the focus forward or back. In my case I get far sight in the upper center near sight in the lower center and towards the edges and middle sight in a roughly H-shaped area in the very center and along the left and right edges.
There's apparently many progressive lens designs, but they are all compromises between conflicting goals. Add the astigmatic correction for people like me and the lens surface will get quite complicated.
We don't look through a point in the glasses, but through a whole area, so a single point in the lens may both be part of the lower edge of the concave near-sighted area toward the top, and part of the convex presbyopic area at the bottom at the same time. This is actually very complicated you want the change to be gradual, without too much visual bending, blurring or other weird effects during the transformation. Instead we have progressive glasses, so named because they go smoothly from a nearsighted concave lens toward the top to a convex (or at least less concave) lens at the bottom. While they're really the best type of glasses, they're not well liked. That gives you those characteristic half-moon bifocal glasses that people instantly recognize as "old-folks glasses". The traditional - and still best - method is simply to "cut out" the lower central part of concave lenses for near-sightedness and replace with convex lenses for presbyopia. That's a hassle, though, so you'd really like to combine them into one pair. You could have two pairs of glasses of course, and switch between them. People that have astigmatism as well - like me - need glasses at all viewing distances, so removing your glasses doesn't help much. But once the presbyopia worsens it's no longer enough. Since glasses for near-sightedness worsens presbyopia, people can get around mild presbyopia simply by removing their glasses or looking below or above the rim when they read you see this quite often. This is why they're called reading glasses you can't see far away wearing them so you only use them for close work. A concave lens for near-sightedness worsens presbyopia - it makes the minimum focusing distance longer - while a convex lens for presbyopia worsens focus at infinity. How do you make a lens that corrects for both at the same time? Now, here's a problem: what do you do if you're both near-sighted and presbyopic? As you can see in the figure above, the corrective lenses are opposites: one cancels out the other. With nearsightedness you use a concave lens to get infinity focus. This is sufficient for people with otherwise good eyesight. Cheap reading glasses sold here and there are exactly that 2.
So, with presbyopia you can use a convex lens to get closer focus.
The curve of the concave lens is added to the curve of our own lens, effectively making the combination thicker. The way to fix this is with a convex lens like the one on the right that will help make the eyes stronger. Presbyopia is the inability to focus close, and at the bottom we see the reason for it: as we age the lens gradually hardens, and it can no longer thicken enough to bend the light for close objects. Think of it as the curve of the convex lens being subtracted from the curve of our own lens. We can fix this with a convex lens, like the one on the right, that'll effectively weaken our own lens and let us focus far away. Even when the lens is as flat as possible it still bends light too much to bring far-away things into focus. At the top we see the cause: the retina in the back of the eye sits too far away from the lens. Like many, many other people, I'm near-sighted.