WASHINGTON (NYTIMES) - Carrots or sticks? Aid or sanctions? Engagement or containment?

American attempts to counter North Korea's nuclear programme did not begin last week when President Donald Trump promised to unleash "fire and fury" against the isolated government.

For decades, Mr Trump's predecessors have waded into the diplomatic mire, trying to threaten or cajole North Korea's ruling family into abandoning the country's weapons programs. Each failed.

North Korea, which conducted its first nuclear test in 2006, has detonated five test bombs and is expected to explode a sixth. Since 1993, the country has also launched a series of missiles, improving their distance, accuracy and lethality each year.

Despite the North's weapons tests and its bellicose bluster, the country has occasionally signalled a willingness to talk.

THE CARRORT: OIL AND AID (BILL CLINTON)

The early 1990s brought the Korean Peninsula to the brink of war.

North Korea threatened to withdraw from the 1970 Nuclear Non-proliferation Treaty and begin to reprocess plutonium - both of which it eventually did.

In 1993, the North launched a missile capable of hitting Japan. Former President Jimmy Carter went to negotiate with Mr Kim Il Sung, the North Korean leader, against the wishes of President Bill Clinton.

The deal, which Mr Carter struck and Mr Clinton would eventually agree to soon after Mr Kim's death, amounted to a generous offer.

Mr Clinton promised to lift decades-old sanctions, supply the North with 500,000 tons of oil a year and provide US$4 billion in aid to construct a light-water reactor capable of producing nuclear energy but not weapons.

In exchange for the reactor and oil, the North would end its weapons programme and close - but not dismantle - the Yongbyon complex.

Weeks after the agreement took effect, Republicans swept Congress in the 1994 midterm elections. Congress delivered, but often delayed, promised oil shipments and refused to lift sanctions, and the light-water reactors were never built.

By 1998, the North had secretly restarted its weapons programme with technology purchased from the Pakistani scientist A.Q. Khan, and by 2003, the agreement was completely abandoned.

The lesson was an important one for North Korea. By provoking the West, the government had profited: It received several years of free oil and kept its nuclear power plant intact. The US spent millions in aid and only briefly delayed the North's weapons programme.

THE STICK: PUNISHING SANCTIONS (GEORGE W. BUSH)

President George W. Bush confronted the North for secretly building a bomb and violating the terms of the agreement.

In 2002, in his State of the Union address, Mr Bush called North Korea, Iraq and Iran an "axis of evil". The administration hoped to overthrow the government of Mr Kim Jong Il by imposing punishing sanctions.

Mr Kim responded by announcing in 2003 that his country possessed a nuclear device and would withdraw from the Nuclear Non-proliferation Treaty. That announcement ultimately brought the US back to the negotiating table.

In 2005, Mr Kim appeared to agree to a proposal made through the six-party talks - consisting of representatives from China, Japan, North Korea, Russia, South Korea and the US. The deal, which was briefly enforced, traded food aid for a suspension in weapons building, and the US removed North Korea from its list of state sponsors of terrorism.

By 2006, the North Koreans had tested a bomb and were found to be exporting weapons technology to Syria.

The North Koreans successfully gamed the US. As the Bush administration waited for the country to collapse under the weight of sanctions, Mr Kim successfully developed a nuclear weapon, shifting the stakes of all future courses of action.

NEITHER CARROT NOR STICK (BARACK OBAMA)

Just months into President Barack Obama's first term, the North detonated a series of nuclear bombs.

Rather than negotiate, Mr Obama imposed a policy of "strategic patience", hoping that through sanctions and espionage, the US could wait out the isolated state. He hoped that the North would eventually feel it had reason to negotiate and make a good-faith effort at talks.

Instead, the North pursued its weapons programme and launched a series of cyberattacks on American businesses, including Sony Pictures.

Mr Obama also talked tough with the North Koreans when he thought it necessary: In 2014, he warned that the US "will not hesitate to use our military might" to protect US allies.

It was during the Obama administration that Mr Kim Jong Un, a grandson of the country's founder, was named leader after the death of his father, Mr Kim Jong Il.

The youngest Kim quickly eliminated those who might challenge his leadership and began a programme, using new technology, to develop an intercontinental missile.

The Americans initially hoped the young leader would represent a break from the hardline policies of his predecessors, but instead he doubled down. In September 2016, he tested a nuclear warhead that he claimed could fit on a long-range missile.