Simply put, America is reliant on continued Saudi output of oil and Saudi Arabia is reliant on American dollars. For America, Saudi Arabia is a key regional ally; the Saudis rely on American security and weapons. Decisions made against this interdependence would affect the two countries in 'costly ways'.
Saudi Arabia is a sovereign state, but is bound in its support of an independent Palestinian state. It retains no diplomatic relations with Israel - America's other principal ally in the region. It can do little more than make proposals on the matter - even being forced to drop its boycott of Israeli goods.
America is an important supporter of human rights and democracy, but criticisms of Saudi Arabia are rare. This is despite it not only being one of the most repressive and authoritarian regimes in the world, but also intervening in other countries such as Bahrain to control protesters against a similarly authoritarian government.
Multiple channels connect the two countries but mostly through economic and security concerns. Saudi Arabia has, since 2000, spent over $100 million on lobbying groups in the US according to the FARA database. There are also numerous non-state actors such as the US-Saudi Arabian Business Council.
Issues have had varied importance, and though oil has been a dominant force in the relations, security concerns have often been briefly prioritised for both countries. Such examples include the current Syria crisis (where Saudi Arabia supports the Sunni population), the on-going 'War on Terror', and Saudi need for American arms and weapons. Worth mentioning too, is the historical presence of US troops within Saudi Arabia.
