Something of a client state or co-dependency.

The US relies on Saudi oil.

Saudi Arabia relies on US protection.

Each benefit mutually from petrodollar pricing -- the US guards against devaluing its currency (and reducing the value of dollar-denominated assets within its financial system), Saudi Arabia, and virtually every oil-exporting nation, benefits by not having their currencies appreciate in the absence of any meaningful domestic demand for foreign goods.

There are other elements, though those are the large ones.