Twelve years after they ended their eight-year war, both sides accuse each other of holding onto their prisoners of war.
Iraqis are welcoming the news that Iran's foreign minister will soon visit Baghdad.
On Sunday, Iraq's official newspaper, Babel, said the two countries had agreed to resolve their differences after Iraqi Vice-President Taha Yassin Ramadan met Iran's President Mohammad Khatami in Venezuela.
No date has yet been given for the visit, but Iraqis are hoping it will end years of mutual distrust.
Iraq's Foreign Ministry is keeping tight-lipped about the forthcoming visit. They have confirmed that it will happen, but they will not say when.
Outstanding business
Nor will they say exactly what he is going to discuss; but the issues outstanding between these two Middle Eastern giants are well known.
Twelve years after they ended their eight-year war, both sides accuse each other of holding onto their prisoners of war.
Although more than 10,000 Iraqis have been repatriated from Iran in recent months, the issue is still an emotive one.
The International Committee for the Red Cross says it is still dealing with hundreds of cases in both countries.
Opposition groups
Another bone of contention is the violent opposition groups that shelter on either side of the joint border.
Bombs have gone off in both countries this year. Iraq blames Tehran for harbouring the perpetrators; Iran blames Iraq for doing the same.
Iraqis believe that once these issues are cleared up, the two countries could form a powerful economic alliance.
Both their economies depend on oil and both have resisted Western pressure to bring down the oil price.
Iraq and Iran also share an animosity to the United States and Israel.
Their hardline opposition to the current Middle East peace process has helped keep them isolated from much of the world. But whenever the peace process is in trouble, as it is now, Iraqis say their misgivings are justified.