Rezaian was arrested in July 2014. His detention is longer than that of the diplomats and American citizens taken hostage in Tehran in 1979. Three other Americans are also being detained or are unaccounted for in Iran, all of them for longer than Rezaian.
Here are their narratives.
That death sentence was later overturned by a higher court, but he was subsequently convicted in a secret trial of "cooperating with hostile governments" and received a 10-year prison sentence, according to the website and a CNN interview with Hekmati's sister, Sarah, in 2014
Hekmati has been in custody in Iran longer than any other American, imprisoned just weeks after he arrived there in August 2011 to visit his grandmother, the family's website says.
Hekmati flatly denies spying for the United States. He was born in Flagstaff, Arizona, grew up in Flint, Michigan, and served in the Marines from 2001 to 2005 as an infantryman and an Arabic and Persian linguist, the family's website says.
During his detention, he has lost nearly 30 pounds and has trouble breathing, according to his brother-in-law. He might have a lung infection, and his family worries that if Hekmati is not treated, he could contract tuberculosis.
Hekmati's sister and her husband, Ramy Kurdi, traveled to Vienna, Austria, where the nuclear negotiations
were held earlier this year, to make sure Amir Hekmati's case wasn't forgotten.
White House Press Secretary Josh Earnest acknowledged in July that U.S. diplomats have brought up the cases of Americans being detained in Iran on the sidelines of the nuclear negotiations.
President Barack Obama said that tying the release of the Americans to the nuke deal would have encouraged the Iranians to seek additional concessions.
Obama gave a pointed response to one reporter's question
about the four Americans at a news conference in July.
"The notion that I'm content as I celebrate with American citizens languishing in Iranian jails ... that's nonsense, and you should know better," the President said.
Obama noted that he has met with families of some of the Americans held in Iranian custody, and that his administration is "working diligently to try to get them out."
Hekmati's ordeal began when he traveled to Iran to visit his family's ancestral home and spend some time with his ailing grandmother.
"We know there is a risk involved," his mother, Behnaz Hekmati, told CNN in 2013.
Days before he was arrested, Hekmati called his mother and said that he would be coming home. He planned to leave two days after a goodbye gathering his relatives were planning.
He never showed up at the party.
Hekmati was detained in August 2011.
Hekmati family members say that they initially remained quiet about the arrest at the request of Iranian officials who promised his release.
Months after being detained, Hekmati appeared on state television and said he was working for the CIA.
Behnaz Hekmati has said all along that her son's confession was fabricated and forced by his Iranian captors, a position that's supported by the State Department.
The State Department has said Amir Hekmati's imprisonment follows a pattern by the Iranian regime, which it says "has a history of falsely accusing people of being spies, of eliciting forced confessions, and of holding innocent foreigners for political reason."
Hekmati was eventually able to get a handwritten letter
out of prison in which he proclaimed his innocence.
In the correspondence -- dated September 1, 2013, and addressed to Secretary of State John Kerry -- Hekmati says that he has "been held on false charges based solely on confessions obtained by force, threats, miserable prison conditions, and prolonged periods of solitary confinement."
Hekmati's friends and family worry that if he's not freed soon, he may miss his last chance to see his dying father. Ali Hekmati is suffering from brain cancer and has had two strokes since his diagnosis, according to Kurdi, Amir Hekmati's brother-in-law.
"I want my dad to hold his son again. I want my mom's heart to stop breaking," Sarah Hekmati said, fighting back tears. "I want the hole that we all feel by his absence to be filled."
The missing contractor: Robert Levinson
a former FBI agent and contractor for the CIA, vanished after visiting Iran in 2007. Iranian officials have denied any knowledge of his whereabouts.
In March 2007, Levinson traveled to Kish Island and checked into a hotel, according to State Department officials. Levinson was reportedly in the Mideast to investigate cigarette smuggling on behalf of a client. During the visit, he met with American fugitive Dawud Salahuddin, who is the last person to acknowledge seeing him, the officials said.
Levinson had been hired as a contractor by Tim Sampson, head of the Illicit Finance Group within the Office of Transnational Issues at the CIA, one year earlier to write reports for the agency. Three CIA employees, including Sampson, later lost their jobs for overstepping their authority as analysts and withholding information about Levinson after he disappeared.
Levinson's wife, Christine, met with government officials in Iran in late 2007 but did not learn anything about her husband's disappearance.
The CIA paid the Levinson family more than $2 million in 2008 to head off a lawsuit, according to family attorney David McGee.
In the years since Levinson went missing, his family has released video and photos that they say prove he is alive.
In a December 2011 video, Levinson said, "I have been treated well, but I need the help of the United States government to answer the requests of the group that has held me for 3½ years. And please help me get home. Thirty-three years of service to the United States deserves something. Please help me."
A series of photographs the family said it received in April 2011 showed a bearded, shackled Levinson, wearing an orange jumpsuit and holding signs written in broken English.
Hillary Clinton, while serving as U.S. secretary of state, said in 2011
that the State Department had received "indications" that Levinson was being held in South Asia.
During his career at the FBI, Levinson specialized in investigating organized crime in Russia.
The FBI has increased the reward for information on Levinson to $5 million.
Levinson's son, Daniel, testified at a House Foreign Affairs Committee hearing in June.
"We believe that if the Iranian government had the will and motivation to locate my father and send him home, they most certainly could," he said. "My family will never rest until our father is back home with us."
Noting that his father was still a U.S. government contractor at the time of his disappearance, Daniel Levinson stated: "The U.S. has a moral obligation to help bring him home."
Levinson has seven children. He suffers from diabetes and high blood pressure, among other illnesses, according to his family.
Wife Christine Levinson implored the United States and Iran to keep working together -- "with the same sense of urgency" they applied to reaching a nuclear deal -- to free her husband.
"Bob has been held against his will for eight years," she said. "This nightmare must end."
The convert from Islam: Saeed Abedini
Saeed Abedini, an American Christian pastor, was born in Iran and lived in Idaho. He was detained in Iran on September 26, 2012, according to the American Center for Law and Justice.
Abedini's charges stemmed from his conversion from Islam to Christianity more than a decade ago and his activities with home churches in Iran, according to the Washington-based group dedicated to protecting religious and constitutional freedoms.
In 2013, Abedini was sentenced to eight years in prison on charges of attempting to undermine the Iranian government.
His wife, Nagameh, joined the three other families on Capitol Hill in June to plead for the safe return of their loved ones.
Nagameh Abedini told lawmakers at a House Foreign Affairs Committee hearing that raising the case with Iranian counterparts on the sidelines of nuclear talks wasn't enough.
"I appreciate that they're being discussed on the sidelines, but they're still not home," she said. "Where's the action? Where's the result?"
Obama met with Naghmeh Abedini and the couple's two young children -- Rebekka and Jacob -- in Boise, Idaho, in January. The President reassured her the case was a high priority.
The center reported in June that Abedini was beaten by fellow prisoners in an unprovoked attack as he was leaving his cell. He suffered injuries to his face. The center said he has endured torture and numerous beatings, sometimes at the hand of prison guards. At one point, reports circulated about death threats targeting Abedini from ISIS prisoners held at the same Iranian facility.
In 2009, Abedini was arrested in Iran and later released after formally pledging to stop organizing churches in homes. He returned to Iran three years later to help build a state-run secular orphanage. It was during that visit that he was abruptly pulled from a bus and imprisoned.
"My children have desperately missed the loving embrace of their father for the last three years of their lives. They have grown up almost half of their lives without their father," Nagameh Abedini said in a statement, pleading with Congress to keep the detained Americans in mind as it reviews the deal. "Please help us ensure the remainder of their childhood includes both a mother and a father."
The journalist: Jason Rezaian
And finally, the case of Rezaian, the Washington Post bureau chief in Tehran. He, his wife, Yeganeh Salehi, and two freelance journalists were detained on July 22, 2014, according to the newspaper. An Iranian official confirmed to CNN at the time that the group was being held but did not state the charges against them.
The two freelance journalists were released over the next two months, a source close to the family of the detainees told CNN. And in October 2014, the Post reported, Rezaian's wife was released on bail.
Rezaian was eventually charged with espionage and other serious crimes including "collaborating with a hostile government" and "propaganda against the establishment," according to the Post.
The newspaper has rejected the allegations.
"Any charges of that sort would be absurd, the product of fertile and twisted imaginations," the Post said in a recent statement.
The U.S. State Department has called the charges "absurd."
Rezaian was denied bail. And for months, he has been denied access to proper legal representation, according to his family.
Rezaian's trial began in May under a cloak of secrecy.
The journalist has not been allowed to see visitors aside from his wife and has endured long interrogations, family members have said.
Rezaian had been accredited by the government to work as a journalist for the Post since 2012, the newspaper said.
"The only thing that has ever been clear about this case is Jason's innocence," Washington Post executive editor Martin Baron said in a statement in July. "If a ruling has been issued and is now being reviewed, this puts on the onus on Iran's senior leaders to demonstrate the fairness and justice that could only lead to Jason's exoneration and release.''