We bought these for toilet training our 3 year old at night so we didn't need to keep washing sheets every day (and also changing them every night). It says on the instructions to put under the sheet, which we'll probably do once our little one has gotten a bit better at getting up for the toilet (she's a really deep sleeper). For now we put them over the sheet, which works fine as the side they lie on (the absorbent side) is very soft. Because they are waterproof this allows us to quickly change them in the middle of the night without the sheet getting wet. They tuck in nicely to the bed under the mattress so they don't move when the kids roll about (this is a single bed not a smaller cot bed and don't have many issues with it staying in place, occasionally when they're particularly restless they don't stay tucked in). Been using them for nearly a year now, very happy with them, never had to change the sheet due to it being wet. They're very compact so easily thrown in a bag for travelling.
Also tried the Huggies version, nowhere near as good (from what I remember they weren't as big, seemed to make my little one warm and had to be stuck down which I wasn't keen on).