While we know there is no official political relationship between Iran and USA, I want to know about the last one. I do not know about unofficial meetings or phone calls which may happen.
As a consequence of the hostage crisis,
On April 7, 1980, Carter severed diplomatic relations between Iran and the United States and they have been frozen ever since.
US don't have an embassy in Iran, and Iran has no embassy in the US. Heads of states of both sides have never met in the last 40 years.
However, especially during the Obama administration and after Rohani's election, diplomatic talks have been staged and lead to the Iran Nuclear Iran Deal. The highest level of these encouters included ministers of Foreign affairs, hence a governmental level.
You can see here an official meeting between ministers of Foreign affairs Mohammad Javad Zarif (Iran) and John Kerry (USA), held in Lausanne, 2015, and leading to the Joint Comprehensive Plan of Action, or Iran Nuclear Deal.