FACTBOX - Ups and downs of Iraq-Iran relations

(Reuters) - Mahmoud Ahmadinejad arrived in Baghdad on Sunday, the first Iranian president to visit Iraq since the two neighbours fought a protracted war in the 1980s in which a million people were killed.

Tehran's influence over Baghdad has grown since the U.S.-led invasion toppled Iran's long-time enemy Saddam Hussein in 2003. Following are details about relations in the past 30 years:

* IRAN-IRAQ WAR:

-- September 1980 - Iraq accused Iran of shelling Iraqi border towns from territory belonging to Baghdad under the 1975 Algiers accord on the frontier line and Shatt al-Arab waterway. Saddam Hussein tore up the accord and his troops invaded Iran.

-- March 1988 - Iran seized the town of Halabja in northeast Iraq. Tehran said Iraq used chemical weapons to punish inhabitants for not resisting. About 5,000 people were killed.

-- August 1988 - The Middle East's longest armed conflict in modern times ended with a U.N.-sponsored ceasefire. About one million people were killed in a conflict which involved trench warfare, chemical attacks and mass Iranian frontal assaults.

* GULF WAR:

-- August 1990 - Iraq invaded Kuwait. Days later Saddam told Iran he would withdraw from occupied Iranian territory and formally settle the 1980-88 war.

-- January 1991 - Iraq flew more than 140 aircraft to Iran to avoid their destruction before a U.S.-led attack to force Iraqi troops out of Kuwait. Iraq's air force commander said in 2007 he hoped Iran would return some Iraqi warplanes.