This topic will be incomplete without mentioning the good old dulfersitz method used by our fathers when there were no belay plates and no carabiners.
This method doesn't require any equipment other than the rope itself. And, well, sturdy clothes.
The method is to pass the rope around your body in a special way shown in the picture 1 below. Picture 2 shows a variation with a carabiner.
(origin: commons.wikimedia.org/wiki/File:Corda_alpinismo.jpg)
This is a "last resort" type method, because it is quite hard on your body on inclined slopes and simply painful on verticals. But it works and you can even use a prusik to back it up.
Because the rope presses hard on your leg and eats up your clothes by friction, people started to add more fabric to their pants at the main friction point. Then they started to sew metallic parts to their pants. Then they realized that they didn't need pants if they had metallic parts. This way the first belay devices were born.