The Guardian and The Washington Post articles refer to collection of communications pursuant to Section 702 of the Foreign Intelligence Surveillance Act. They contain numerous inaccuracies.
Section 702 is a provision of FISA that is designed to facilitate the acquisition of foreign intelligence information concerning non-U.S. persons located outside the United States. It cannot be used to intentionally target any U.S. citizen, any other U.S. person, or anyone located within the United States.
Activities authorized by Section 702 are subject to oversight by the Foreign Intelligence Surveillance Court, the Executive Branch, and Congress. They involve extensive procedures, specifically approved by the court, to ensure that only non-U.S. persons outside the U.S. are targeted, and that minimize the acquisition, retention and dissemination of incidentally acquired information about U.S. persons.
Section 702 was recently reauthorized by Congress after extensive hearings and debate.
Information collected under this program is among the most important and valuable foreign intelligence information we collect, and is used to protect our nation from a wide variety of threats.
The unauthorized disclosure of information about this important and entirely legal program is reprehensible and risks important protections for the security of Americans.
James R. Clapper, Director of National Intelligence
Note that he says only foreigners outside the U.S. can be "targeted." But that's not quite what happens, according to the Washington Post:
Even when the system works just as advertised, with no American singled out for targeting, the NSA routinely collects a great deal of American content. That is described as “incidental,” and it is inherent in contact chaining, one of the basic tools of the trade. To collect on a suspected spy or foreign terrorist means, at minimum, that everyone in the suspect’s inbox or outbox is swept in. Intelligence analysts are typically taught to chain through contacts two “hops” out from their target, which increases “incidental collection” exponentially. The same math explains the aphorism, from the John Guare play, that no one is more than “six degrees of separation” from any other person.
The Post has updated their report signficantly since posted earlier, so it's worth a reread.