(Reuters) -The United States has pulled some diplomatic staff and military families out of the Middle East, citing unspecified regional security risks.

Its long-running rivalry with Iran may be part of the heightened tensions. This article shows what's behind the rivalry, how it has played out and why tensions are flaring again.

WHY DID IRAN AND THE UNITED STATES BECOME FOES?

Iran and the United States were friends for most of the 20th century.

As the Cold War took hold in the 1950s, Washington relied on Iran's reigning Shah to help stem Soviet influence spreading in the oil-producing Middle East.

The Shah was growing unpopular at home and in 1953 the CIA helped topple a populist Iranian prime minister, Mohammed Mossadegh, who had nationalised Iran's British-owned oil company and wanted a more neutral Cold War stance.

When Iranians overthrew the Shah in 1979, the Islamic revolutionaries who took over accused the CIA of having trained the Shah's secret police and vowed to battle Western imperialism in the region, branding America "the Great Satan".

Revolutionary students seized the American embassy and took dozens of diplomats and other staff hostage for more than a year, ending a strategic alliance that had shaped the region for decades.

HOW DID THE US-IRANIAN RIVALRY PLAY OUT?

The new Iranian government wanted to export its Islamic Revolution to fellow Shi'ite Muslims and groups opposing Israel, which it saw as the chief avatar of a Western imperialist project oppressing Muslims in the Middle East.

Iran's Islamic Revolutionary Guards Corps set up Hezbollah in Lebanon in the early 1980s and the United States accuses the group of bombing its embassy and marine barracks in Beirut in 1983, killing around 300 people, mostly Americans.

Hezbollah, which went on to fight repeated wars with the main U.S. regional ally Israel, has said other groups were responsible.

Iran had complaints too. Iraq invaded Iran in 1980 and started using chemical weapons against Iranian soldiers and border villages from 1982 but Washington lent diplomatic backing in the war to Baghdad. A U.S. warship also mistakenly shot down an Iranian passenger plane in 1988, killing 290 people.

Tensions eased after 1990, as the U.S. focused on Iraq after Baghdad's invasion of Kuwait and as Iran in 1997 elected reformist President Mohammed Khatami, who sought better relations with the West.

The rivalry heated up again in the early 2000s with U.S. President George W. Bush labelling Iran part of an "Axis of Evil" along with Iraq and North Korea, a tag that caused anger in Iran.

Iran's secret nuclear programme was revealed in 2002, while the U.S.-led invasion of Iraq in 2003 put the two countries on opposite sides of a struggle for control in the Shi'ite majority country.

WHO DO THE U.S. AND IRAN BACK IN THE MIDDLE EAST?

The U.S.-Iranian rivalry has often played out at arm's length in conflicts and political struggles between each side's proxies and allies around the Middle East.

Besides Hezbollah, Iran backs armed Shi'ite factions in Iraq that have attacked U.S. forces there, the Houthi group in Yemen that has attacked international shipping in the Red Sea and the Palestinian militant group Hamas.

The United States is the main international backer of Israel, Iran's biggest regional foe. It is also a close ally of Sunni Gulf monarchies which for years pursued their own rivalry with the Islamic Republic, seeing it as their main regional threat.

Although Saudi Arabia and other Sunni kingdoms have buried the hatchet with Tehran, they remain wary and fear that any U.S. strikes on Iran could prompt retaliation against them.

HOW DOES IRAN'S NUCLEAR ISSUE FIT IN?

The revelation that Iran was secretly enriching uranium - a process to generate fuel for an atomic power plant but that can also make more concentrated material needed for a bomb - put its nuclear programme in the U.S. crosshairs.

Western countries ramped up pressure on Iran with sanctions as negotiations over its nuclear programme meandered for years.

Iran says its programme is entirely civilian and that it has the right to enrich uranium. Washington and its allies say Iran has consistently hidden important elements of its programme and believe it wants to build a nuclear bomb.

In 2015 Iran and six major powers including the United States agreed to curb Tehran's nuclear work in return for limited sanctions relief, but U.S. President Donald Trump ripped up the deal in 2018.

The two sides are negotiating again but seem far apart and Trump has threatened to bomb if there is no new deal.

WHY IS ISRAEL'S STANCE ON IRAN IMPORTANT?

Israel has often described Iran as its most dangerous enemy and has indicated it may strike the country's nuclear sites.

Any such attack would likely need U.S. acquiescence, potentially dragging Washington into a conflict with Tehran.

Israel is already widely seen as behind covert attacks on Iran's nuclear programme including the Stuxnet computer virus and assassinations of scientists. Israel has neither confirmed nor denied this.

Tensions have increased since the Hamas attack on Israel on October 7, 2023 and as war raged in Gaza.

Last year Israel defeated Tehran's main regional ally Hezbollah and struck Iranian military targets in Syria and Iraq. Iran's Houthi allies in Yemen targeted Israel with strikes.

Iran and Israel twice exchanged direct fire with missiles and drones, underscoring the possibility of a full-blown war.

(Writing by Angus McDowall, Editing by Timothy Heritage)