Take a minute and update your profile with some kind of location so people can better answer your question.
In our area, NE Ohio, for a typical foundation with concrete footers, the footers are poured on the excavated grade. There is no gravel between the grade and the concrete footing. There is a basement wall system called 'Superior Wall' that doesn't use a traditional footing, but instead places precast concrete walls on a tamped gravel base. That is an engineered system, not to be confused with what you asked.
If you are planning on building your own house, and have a lot of questions like this, I would recommend finding a good local architect in your area and let him/her design your house. They will normally detail the print on how specific areas of the house are to be built. Foundations differ depending on where you are. You only have one chance to do it right. Very important part of the house.