The very existence of National Security Agency (NSA) was not revealed for more than two decades after its establishment in 1952, and even now its structure and activities remain largely unknown. Hence its wry nickname: No Such Agency.

Of all the US intelligence services, it is has been the best hidden, and has prided itself on having the fewest leaks – at least until now. How many people does it employ? That is classified. Just how many people does it target? The NSA tells members of Congress that it does not have the tools to provide such figures.

When Harry Truman set up the NSA, it was exclusively aimed at monitoring communications abroad. The question that had exercised politicians and civil rights organisations since the Senate unveiled it in 1975 is to what extent its ferocious appetite for data has encompassed American citizens. General Lou Allen, the first NSA chief to appear in public, told Congress in the mid-1970s that the agency maintained lists of hundreds of names, including US citizens under surveillance for anti-war dissent or suspicious foreign connections.

As technology has evolved, so has the NSA's capacity to intercept an astonishing variety and volume of communications. Satellites scoop up calls and emails in the ether and beam the information back to earthbound receiving stations. One estimate suggests that each of these bases hoovers up roughly one billion emails, phone calls and other forms of correspondence every day, and the agency has up to 20 bases.

"This is not science fiction. It is happening now," a source with knowledge of the NSA said.

Domestic snooping exploded in scale after 9/11, when George W Bush authorised the agency to eavesdrop on Americans without the previous requirement for warrants. Within a few months of taking office in 2009, the Obama administration's Justice Department conceded that the agency had been guilty of "over-collection" of domestic communications but claimed the excess had been accidental.

With every passing administration, the NSA has ballooned. One well-informed estimate of its staffing levels is 100,000, of whom about 30,000 are military and the rest private contractors. Its headquarters is a vast edifice of smoked glass in Fort Meade, in the leafy Washington suburbs, with sizeable complexes in Georgia and Texas and overseas bases in Japan, Germany and the UK.

While the NSA is by far the biggest surveillance agency in the world, it shares some of its work with four other allies: Britain, Australia, New Zealand and Canada. Collectively, they are known as the "five eyes". Of the five, the biggest after the NSA is Britain's General Communications Headquarters (GCHQ).

The predecessor to the NSA was the short-lived Armed Forces Security Agency, which was set up in 1949. It was a relatively modest body compared with the mammoth the NSA has since become.

The young agency suffered some early embarrassments. In 1960, two of its staff defected to the Soviet Union. Three years later, a former NSA employee published code-breaking secrets in the Soviet paper Izvestia; the same year, an NSA employee killed himself while being investigated for selling secrets to Moscow.

Since then, internal security has been tightened significantly, but as the agency's secrecy deepened, its reach expanded relatively unchecked. It was a Democratic senator and lawyer, Frank Church, who in 1975 first raised the alarm at the agency's sprawling tentacles. During a series of hearings into the work of the intelligence agencies, he warned that the NSA's magnifying glass could be turned inwards on the American people.

"I don't want to see this country ever go across the bridge," he said. "I know the capacity that is there to make tyranny total in America, and we must see to it that this agency and all agencies that possess this technology operate within the law and under proper supervision, so that we never cross over that abyss. That is the abyss from which there is no return."

The Church Senate hearings led to the 1978 Foreign Intelligence Surveillance Act (Fisa), which required a warrant to conduct surveillance of communications within the US. A Fisa court, made up of a small group of judges appointed by the chief justice and located inside in the justice department, was given the job of deciding whether to grant warrants – it approves almost all requests.

In the years since 9/11, as the role of the NSA has snowballed, so has the debate over its operations. In 2005, the New York Times reported that the Bush administration had secretly authorised the NSA to eavesdrop on Americans and others inside the US, to search for terrorist activity without the Fisa court warrants. The order had been signed in 2002, but the newspaper cited about a dozen serving or former officials who expressed concern about the legality. The Times delayed publication of the article for a year because of government concerns about its impact.

In the face of the subsequent uproar, the Bush administration said it had ceased the warrantless surveillance in January 2007 and resumed the practice of requiring NSA warrants. In 2008, Congress loosened some of those constraints in the Fisa Amendment Act.

The massive surveillance programme has continued under the Obama administration, at home as well as abroad. And the culture of intense secrecy persists. For years, Senators Ron Wyden and Mark Udall have been demanding to know just how many people inside the US have been spied on by the NSA. No answer has been forthcoming.