The U.S. has long had a love-hate relationship with Pakistan, sending it billions of dollars in aid while suspecting, and occasionally accusing, Pakistan’s intelligence agency, the ISI, of supporting terrorist groups.

The evidence and allegations of those connections have been coming so quickly it’s been hard to keep track of it all. What exactly are the United States' claims? What proof does it have, and which groups does it suspect the ISI has collaborated with? Here’s our breakdown of the basics. (And here’s an earlier guide we did as well.)

The latest U.S. accusations against Pakistan

On Sept. 13, members of a Pakistan-based insurgent group called the Haqqani network laid siege to the U.S. embassy and NATO headquarters in Kabul, Afghanistan.

A detailed New York Times piece on the Haqqanis described them as “the Sopranos of the Afghanistan war, a ruthless crime family that built an empire out of kidnapping, extortion, smuggling, even trucking.”

The attack lasted 20 hours and killed 27 people, including insurgents. It was the most direct attack on the U.S. embassy since it reopened almost a decade ago. American officials told the New York Times that the attackers had placed calls to Pakistani intelligence agents from their cell phones.

Shortly after the attacks, Defense Secretary Leon Panetta criticized Pakistan for providing a safe haven to the Haqqani network and said that the United States would do “everything we can to defend our forces.”

On Sept. 22, Adm. Mike Mullen, the outgoing chairman of the Joint Chiefs of Staff, went much further. He accused Pakistan’s intelligence service of directly supporting the apparent Haqqani attacks in Kabul. Mullen also said the ISI provided support for two other recent attacks: a large truck bombing Sept. 10 and an attack on a Kabul hotel in June.

Mullen told the Senate Armed Services Committee that while the ISI does not have operational control over the Haqqani network, it is “in many ways, a strategic arm of Pakistan’s Inter-Services Intelligence Agency” and operates from Pakistan “with impunity.”

U.S. officials have long suggested that the ISI has kept ties with the Haqqanis as a way to maintain influence in Afghanistan, though none has been as blunt as Mullen was. Pakistan is worried primarily about India and views the Haqqanis as a handy proxy force to counter Indian influence in Afghanistan.

Pakistani Prime Minister Yousuf Raza Gilani denied the accusations. Some U.S. officials, speaking on condition of anonymity, have criticized Mullen’s comments, saying they overstate the situation.

The United States has been frustrated for some time with the Pakistani military’s reluctance to engage militants in North Waziristan, a mountainous area of Pakistan where groups that attack U.S. targets in Afghanistan have found refuge.

Though the Obama administration hasn’t provided details on the steps it would be prepared to take, officials have indicated that the United States would be ready to act unilaterally if Pakistan doesn’t crack down on the Haqqani network and other terror groups within its borders.

(Updated: Oct. 3, 2011) According to anonymous U.S. officials, the U.S. itself spoke with a Haqqani network leader shortly before the September 13th attack, in a meeting arranged by the ISI. ABC News learned about the meeting a week and a half after Mullen's controversial remarks, and said the new information "suggests a much more nuanced -- and very often, confounding -- relationship with Pakistan's intelligence service than Adm. Mullen and other military officials have publicly admitted in the last two weeks."  

Pakistan’s intelligence service linked to more attacks

The ISI has been suspected of collaborating with some terrorists for years. A ProPublica investigation detailed links between the ISI and Lashkar-e-Taiba, the group that carried out the 2008 Mumbai attacks that killed 116 and wounded 308, including six Americans. According to trial testimony from David Coleman Headley, a top reconnaissance operative behind the plot, ISI officers helped to fund and plan the attacks and chose American, Western and Jewish targets for Lashkar to attack. The Headley trial marked the first time that U.S. prosecutors had charged an ISI officer with terrorism. You can read our full investigation here.

The New York Times also reported this week that, according to eyewitnesses, a 2007 ambush on American officials was carried out by Pakistani military and intelligence officers. An anonymous U.N. source told the Times that U.S. officials have known this but kept it quiet in the interest of smoothing relations between the two countries. Pakistani soldiers present during the attack claim that a lone, unbalanced member of Pakistan’s border militia opened fire on the Americans.

Pakistan turns a blind eye to other terror groups

As Time magazine detailed this week, Pakistan has also been hesitant to crack down on Lashkar-e-Jhangvi, a terrorist group that carries out attacks mostly within Pakistan. LeJ is known to train with al-Qaida and has links to the Taliban. The group was also involved in the 2002 killing of American journalist Daniel Pearl.

According to Time’s report, the military, provincial government, law enforcement and judicial system have all been unable to hold LeJ accountable, empowering the group to attempt bolder attacks.

The group’s leader, Malik Ishaq, was released from prison in July because of a “lack of evidence,” though he is suspected of coordinating a high-profile attack on the Sri Lankan cricket team from prison. Earlier this week, Pakistan put Ishaq under temporary house arrest, and as of yesterday he is reportedly back behind bars. According to the Agence France-Presse, “rights groups say a persistent lack of action from the government has emboldened sectarian militant groups, blamed for the deaths of thousands in past years.”

Pakistan pushes back

The Pakistani Army announced Monday that it has no new plans to go after the Haqqani network despite increased American pressure.

Prime Minister Gilani said that any unilateral entry of his country by U.S. forces to track down terrorists would be a violation of national sovereignty.

Pakistan has increasingly courted China since the United States suspended and canceled millions in aid earlier this summer. While Pakistan has received U.S. aid since the early days of the Cold War, roughly two-thirds of it has come since 9/11—or $20.7 billion since 2002.

This week, Pakistan’s interior minister offered to help crack down on Chinese militants taking refuge in Pakistan.

Other reports of Pakistani officials aiding terrorists

A recent New Yorker piece about Pakistani journalists who’ve been threatened by the ISI included an interview with Fida Muhammad, an ISI agent who claimed he helped Haqqani fighters travel across the border from Pakistan to Afghanistan. He also claimed that ISI agents had helped a group of insurgents flee from Tora Bora, the area of Afghanistan where Osama bin Laden was hiding in 2001, to Pakistan. From the New Yorker:

Muhammad told me that his most memorable job came in December, 2001, when he was part of a large ISI operation intended to help jihadi fighters escape from Tora Bora—the mountainous region where bin Laden was trapped for several weeks, until he mysteriously slipped away. Muhammad said that when the American bombing of Tora Bora began, in late November, he and other ISI operatives had gone there, and into other parts of eastern Afghanistan, to evacuate training camps whose occupants included Al Qaeda fighters.