After much hype and speculation, President Barack Obama did not share a historical grip with Iranian President Hassan Rouhani, who skipped out on the United Nations luncheon. But, while a handshake and conversation between the two leaders was characterized as “too complicated” to happen over tuna tartare, relations between the U.S. and Iran may continue to see improvements.

President Obama has already exchanged letters with President Rouhani. And the democratically elected president has already proven more moderate than his predecessors—he’s tweeted a Rosh Hashanah greeting, released dozens of political prisoners, and says a citizens' rights charter is on the way. Nonetheless, Iran’s nuclear ambitions, conservative “old guard,” three decades of impasse, and many other issues still stand in the way of friendly diplomacy.

We talk with Marvin Zonis, a Middle Eastern political expert, about where Tehran stands and where its relationship with Washington is headed.

View a timeline of U.S and Iranian diplomatic relations below.

Yasmin Rammohan contributed to this report.