Article VI is a short, but extremely important part of the core of the United States Constitution. Part of it is no longer necessary. However, the U.S. Constitution cannot be altered. Amendments to the Constitution are additions to the document. Nothing can ever be removed, which is why there remain pieces of the document that do not apply to the modern country. Even nullifying part of the Constitution requires an amendment. In this case, as will become obvious, the parts of the article that became irrelevant resolved themselves.
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The first section of Article VI of the U.S. Constitution involves debts incurred by the United States. It states in so many words that any debts incurred by the United States under the name of the Confederation are upheld as debts of the United States under the Constitution. In short, if the states owed anyone money before the document, they still owe it. While the country is in massive debt, as of 2014, this section is outdated, a Constitutional relic, if you will.
The second section of Article VI is one of the most important statements in U.S. politics. Put briefly, it states that the Constitution and any laws, treaties, etc. formed under the authority of that document are the "supreme" law of the land. In these areas, the federal government trumps state and local government. If the Constitution says yes or no to an issue, that is the answer throughout the states.
The final section of Article VI states that Senators, Representatives, judicial officers, legislators, executive officers, etc. shall be bound by oath to uphold the Constitution. Perhaps more importantly, it goes on to state that "no religious test shall ever be required as a qualification to any office or public trust under the United States." In a country with a strong fundamentalist sect, this part of the Constitution is very important in maintaining separation of church and state that goes hand-in-hand with freedom of religion.