AP In this Sept. 10, 2013 photo released by the official website of the office of the 
WASHINGTON (AP) - President Barack Obama and Iran's new president are scheduled to attend the U.N.'s annual meeting of the General Assembly next week, setting up the possibility of the first exchange between American and Iranian leaders in more than three decades.
Although their disagreements are grave and plentiful, President Hasan Rouhani's recent overtures have raised hopes of a thawing of U.S.-Iranian relations, which have experienced few ups and countless downs since the 1979 Islamic Revolution and subsequent hostage crisis at the U.S. Embassy in Tehran.
No one has confirmed a meeting, though Obama has long said he'd be open to discussion if Tehran shows it is serious about curbing its nuclear program.
A brief history of the long-strained relations between the United States and Iran:
CIA COUP
The aftermath of World War II and the advent of the Cold War make Iran a U.S. policy focus for the first time. Washington sees the country as a bulwark against Soviet expansion and a source of stability in the oil-rich Persian Gulf. It cultivates a friendly relationship with Shah Mohammad Reza Pahlavi. The partnership is threatened with the 1951 appointment of Prime Minister Mohamed Mossadegh, who moves to nationalize Iran's oil industry. A CIA-backed coup ousts Mossadegh in 1953. The shah returns from his brief exile and resumes control.
COLD WAR ALLIES
The United States provides the shah hundreds of millions of dollars over the next quarter-century. The U.S. helps set up Iran's intelligence agency in 1957. Iranians come to revile the agency for its repression. Iran's oil exports expand and the economy grows significantly. The shah recognizes Israel and becomes a dominant figure in the Middle East. Some tensions persist, however. Iran refuses to help the U.S. in the 1970s by lowering the price of petroleum. Toward the end of the shah's reign, the U.S. criticizes his government's worsening human rights record and crackdown on democracy. Still, the U.S. publicly stands by Pahlavi. President Jimmy Carter visits Iran in December 1977 and declares, "Iran, under the great leadership of the shah, is an island of stability."
REVOLUTION
Frustrated by the monarchy's brutality, corruption and autocracy, and faced with economic slowdown, Iranians overthrow the shah in 1979. Ayatollah Ruhollah Khomeini returns from exile, seizes power and declares the U.S. the "Great Satan." The shah seeks exile in the U.S.; Iranians demand he be handed over. In November, militants storm the U.S. Embassy. Fifty-two Americans are held for 444 days. An American rescue operation ends in disaster. Washington freezes billions of dollars in Iranian assets stored in the United States. The U.S. ends diplomatic relations with Iran.
PROXY WARS
Iraq's Saddam Hussein invades Iran in 1980, and the United States provides him with support. Perhaps 1.5 million people are killed over the next eight years, with Hussein even using chemical weapons. The Iranian government kills thousands of political opponents at home and assassinates several higher-profile figures abroad. It gets involved in Lebanon's civil war, providing support to Hezbollah. The new Shiite militant group is blamed for the 1983 bombings of the U.S. Embassy in Beirut and of the Beirut barracks of the U.S. Marine Corps; the two bombings killed more than 250 Americans. Iran places underwater mines in the strategic Persian Gulf. The U.S. responds in 1987 and 1988 by targeting Iranian oil installations, and the Iranians counter with speedboat attacks. Fighter jets skirmish and the two countries approach outright war. In July, the U.S. mistakenly downs an Iranian passenger jet flying above the Strait of Hormuz, killing 290 people, including more than 60 children. In August 1988, Iran and Iraq reach a cease-fire.
IRAN-CONTRA AFFAIR
In the midst of some of the fiercest U.S.-Iranian hostility, the White House covertly sells arms to Iran and uses the proceeds to bankroll a secret war in Central America. Exposed in 1986, the scandal cripples the final two years of Ronald Reagan's presidency.
EXPORTING TERRORISM
Through the 1990s, the U.S. accuses Iran of sponsoring acts of terrorism around the world. Iran and its proxy Hezbollah are blamed for a 1992 attack on the Israeli Embassy in Buenos Aires, Argentina, that kills 29 people, and an attack on a Jewish community center there two years later that kills 85. The U.S. and Israel say Iran provides the critical support for dozens of Hamas suicide attacks and other bombings. President Bill Clinton imposes far-reaching oil and trade sanctions on Iran in 1995.
DIALOGUE AMONG CIVILIZATIONS
The 1997 election of Iran's reformist President Mohammad Khatami offers hope for a thaw in relations. Khatami promotes a "dialogue among civilizations" and reaches out to Western leaders. The U.S. lifts some sanctions on Iran.
POST-9/11 WORLD
Limited U.S.-Iranian cooperation continues after al-Qaida terrorists attack the United States on Sept. 11, 2001. Officials from both sides coordinate before the U.S. invades Afghanistan to oust the Taliban. Months later, President George W. Bush enrages Iran by including it with Iraq and North Korea in his "axis of evil." Washington releases information about Iran's nuclear program and rebuffs Khatami's offer of a "grand bargain" to normalize U.S.-Iranian relations. After the U.S. ousts Iraq's Hussein in 2003 and occupies the country, it accuses Iran of providing Shiite militants with sophisticated weapons to kill American soldiers. The U.S. steers clear of European diplomatic efforts to resolve the Iranian nuclear standoff.
AHMADINEJAD'S ARRIVAL
The election of hard-line conservative Mahmoud Ahmadinejad to the Iranian presidency in 2005 weakens the case for rapprochement in both countries. Ahmadinejad calls for the elimination of Israel and declares the Holocaust a myth. He sends Bush an 18-page letter criticizing the U.S. response to the 9/11 attacks. With Iraq in chaos, U.S. officials reach out to Iranian counterparts for some help in stemming the violence. As America turns increasingly anti-war, Bush and his advisers play down talk of war and join nuclear negotiations between world powers and Iran. At the same time, the U.S. rallies international unity against Iran's nuclear activity. The diplomatic effort yields three rounds of U.N. sanctions between 2006 and 2008 demanding Tehran stop enriching uranium and exporting weapons. They also set banking, trade and travel restrictions on Iran. The Iranians say they won't slow their program, insisting it is intended for peaceful energy production.
OBAMA'S ENGAGEMENT
President Barack Obama takes office in 2009 after raising the possibility of sitting down with Iranian leaders without preconditions. Engagement becomes difficult after Ahmadinejad wins another term in an election many believe is fraudulent and is followed by a violent crackdown. On the sidelines of nuclear talks in October 2009, a senior U.S. official meets privately with a top Iranian negotiator for some of the most extensive bilateral talks in decades. Iran quickly backs out of a deal reached with world powers to ship out much of its higher-enriched uranium.
CRIPPLING SANCTIONS
A fourth round of U.N. sanctions against Iran passes in 2010. Meanwhile, the U.S. and Israel covertly cooperate in a campaign to sabotage Iran's nuclear program. After Syria's civil war erupts in 2011, Iran actively supports Syrian President Bashar Assad while the U.S. slowly escalates aid to the rebels. Obama faces pressure at home and abroad over Iran's nuclear program. He urges patience from Prime Minister Benjamin Netanyahu, who threatens an Israeli military intervention. But Obama also says all U.S. military options are on the table. With engagement failing, he focuses on "crippling" international sanctions. The most severe hit Iran's oil industry, slicing exports in half and leaving the Iranian economy in tatters. Several more rounds of nuclear talks take place, though no progress is made. During his re-election campaign, Obama vows to prevent Iran from reaching nuclear weapons capacity.
MODERATION PREVAILS
Promising a new course of moderation, Hasan Rouhani becomes Iran's new president in August 2013. He exchanges letters with Obama, raising hopes for a nuclear breakthrough. He makes a series of public statements suggesting a new flexibility in talks with the West.
