What is the fundamental problem with US-Iran relations for which they haven't been able to establish a diplomatic relationship even after 38 years?
What does the USA want from Iran, that Iran has been unable to provide and vice versa?
EDIT:
If Iran's patronizing of terrorism and anti-Israel stance are the problems, how is Saudi Arabia getting along?
History: Mohammad Mosaddegh was the democratically elected Prime Minister of Iran from 1951 until 1953 when he was removed from power in a coup on 19 August 1953, organised and carried out by the CIA at the request of MI6: See here.
The US was the main supporter of the ex-dictator of Iran, the Shah, until the 1979 Iran Islamic revolution. The US accepted the Shah, (who had killed tens of thousands), and refused to deliver him for trial. In return, Iranian student occupied the US embassy... .
Two policy based on Two ideology
The new government system of Iran was an Islamic republic. Iran's foreign policy took from slogans that people used to say during demonstrations against Shah: "No to East no to West only Islamic republic" (rejecting Soviet Union and US). On the other hand the US claims that liberal democracy and secularism is the best way of life.
In the region that has the main oil resources of the world, this new system claims that we want to be independent of the West. If this ideology spread among other (Muslim) nations of region, the outcome would be a catastrophe for the US. Pro-US dictators would disappear and independent governments could sell their oil for prices they want.
Iran wants to show that the independent Islamic model is prosperous, and the US wants to show independence is a model of failure.
As an Islamic republic, based on Shia ideology, Iran begin to support the Palestinian and Lebanese resistance against Israel. This was not what the US liked.
Two factors have a big effect here.
On the other hand supporting the Shah and Israel makes the US a demon from the Iranian perspective. Imposing sanctions makes it bitter.
What does the USA want from Iran, that Iran has been unable to provide?
Give up independence. Don't support Hamas and Hezbollah and recognize Israel,... Briefly; Don't be yourself.
What does the Iran want from USA, that USA has been unable to provide?
Don't try to dominate the world. I want to be independent. Don't support Israel,... Briefly; Don't be yourself.
What is the fundamental problem with US-Iran relations for which they haven't been able to establish a diplomatic relationship even after 38 years?
One sovereign nation wants to dictate what the other sovereign nation can or cannot do.
I don't know why my post is removed despite of that I try explain it more.
If you look to history of region, you see that three countries took control of most part of the world and Middle East in different times.
Iran: Before Islam Saudi Arabia: After Islam Turkey: Ottoman time.
And now all those countries have dreams about their golden ages and have competition with the others to take control of Middle East in their hands.
Between those three countries Iran has different conditions. Energy reservoirs, mineral depositions, strategic situation, population, cultural ties with all peripheral countries and agricultural conditions give Iran unique position compare to the others. Turkey doesn't have access to Persian Gulf, doesn't have energy resources and almost people in there are Turk and Kurd. Saudi Arabia doesn’t have access to Caspian Sea area, doesn't have important mineral depositions and doesn’t have powerful agriculture with majority of Arab people. However Iran’s people are Fars, Turk, Kurd, Arab, Baloch, Turkman, Armenian and many others (including other Christians and Jewishs).
I think that Iran's will to control of region, started in 1970s. Iran (or I should say Shah) took leadership of OPEC and they fought for oil price. Among this fight, Mr. Nixon made the petro-dollar deal with Saudi Arabia and other OPEC countries but OPEC (Shah?) won the war at 1974 and oil price rise dramatically. I believe that fundamental of problem between Iran and US was made in that time. And after that US worried about Shah's plans.
Iran started developments plan in all directions. Iran's nuclear program started with help of US and Germany. Iran's army developed rapidly (with particular attention to Air Force) and growth of Iran's economy rose to between 10 and 20 percent for a decay (with producing 6 million-barrel oil per day).
And then Iran started to play a major role in region. For instance: At 1973 Iran started to send troops to Oman to defeat rebellions and the Iranian troop remained in there till Iran's revolution.
Iran's problem with Iraq led to a military conflict and Iraq was defeated in two days. The military conflict led to 1975 contract that was signed by two countries in Algeria. It's interesting that Saddam Hussein signed contract from Iraqi side and in 1980 he ripe off the contract.
Then in last years of 1970s Iran became most important and most powerful country of Middle East, in the time that all countries of region heavily suffered from undeveloped conditions.
Shah got more and more disobedient. He started to establish a military relationship with USSR and bought some armored vehicle from USSR.
To get everything worse, Shah started to crisis west and claims that western countries should change their people life style and they should work harder.
All of these led to Guadeloupe conference.
https://en.m.wikipedia.org/wiki/Guadeloupe_Conference
I think background of decision that was made in Guadeloupe returns to 1953 (Ajax Operation). In That year, CIA made a coup against democratic elected Prime Minister Mohammad Mosaddegh to return Shah to power with help of Islamists, Mobs and some part of army. The coup was successful, but in that time US made fool Ayatollah Kashani and after coup he loses all of his influence.
In last years of 1970s US think that "why we cannot repeat the successful experience of corporation with Islamist?" They thought that this time they could remove Shah from power and then helped to moderate nationalist Islamic parties (Technocrats) to take power (The party that was reborn after coup from remain of the other party that heavily suffered from the coup – Nehzat Azadi). Consequents could be something like this: disobedient Shah would have been removed from power and again an obedient Iran with technocrat’s leadership (educated in west) remains in Western Bloc.
Then Guadeloupe decision was made and Iran faced revolution. But this time everything has changed to compare 1953. Cleric people in Iran didn’t forget that what happened in 1953. Imam Khomeini was far far smarter than that Americans supposed. After revolution, for preventing from something that was happened in 1953, US embassy was captured by Muslim Students Follower’s Imam Line and Iran Hostage Crisis was started on November 4 1979. Only after Hostage Crisis, Mr. Carter realized that Iran was out of control. And after that US did everything to return Iran to Western Bloc but failed completely.
Operation Eagle Claw on April 24 1980
Nojeh Coup on 9-10 July 1980
Iraq Attack on 22 September 1980 to August 1988.
Support Iraq in war in anyway https://en.wikipedia.org/wiki/United_States_support_for_Iraq_during_the_Iran%E2%80%93Iraq_war
Downing Iranian Airbus on July 3 1988 with 290 civilians dead
… … …
Sanctions because of everything
And finally Mr. Trump
Against that Iran did something bad to US too as revenge.
All these not only didn’t get back Iran to Western Bloc but also caused Iran more and more was pushed toward Russia and China.
And now an independent Iran, most stable and most democratic country in middle of disturbed Middle East with close ties with Russia and China, is worst thing that US could imagine.
One factor (the only one I'm mentioning because it is excluded from the other answers) is that each is very convenient to use as an evil political boogeyman to whip up nationalist "enthusiasm" among the masses.
If there is any level of discontent, a need to distract from current state of affairs or news, or momentum for change, nothing rallies the masses around the in-power status quo like uniting against an evil enemy. This applies to both nations, for this particular question.
This can be seen by the way the nations have cooperated militarily against ISIS/ISIL/Daesch, but that cooperation was kept in the background and not spoken of, let alone emphasized, by either government. Usually nations are pretty open and proud of working together towards a common goal. In this case, it would undermine the message and usefulness of the message of the great "enemy."
