All my carpets are Persian, Chinese, Indian or other Islamic.
You can see the wood floor arround the edges. They do not slip if you put them on a proper felt underlay. And most of them are large enough and heavy enough not to move.
They can be removed for cleaning if you wish, but I simply vacuum clean them, and have never thought of anything else (no cats or dogs though). They have the advantage that you can take them with you when you move.
They are between 30 and 70 years old, and I reckon they have at least another 100 years wear in them (except for the Indian, which never was good quality).
Of course, they cost rather more to begin with.
This may not suit everybody, but it does have it's advantages.