Last week, U.S. Special Operation forces headed to a cave in Hagr al-Saiaar, a remote area of Yemen for a rare on-the-ground intervention in the Middle Eastern nation. They were taking part in a rescue mission and hoped to free a number of hostages chained up in the cage and kept prisoner by al Qaeda in the Arabian Peninsula (AQAP), a particularly feared al Qaeda offshoot.

The rescue mission was not a success. While eight hostages were freed after a firefight that left all the kidnappers dead, five hostages who were expected to be in the cave were not there. According to a a member of Yemen's anti-terrorism force quoted on a Web site connected to Yemen's defense ministry, these five hostages included an American and a Briton.

Less than a week later, AQAP released a video that appeared to show the American hostage, a 33-year-old freelance photographer named Luke Somers. Sommers was filmed pleading for his life, while an al-Qaeda official said that Somers will meet his “inevitable fate” unless demands are met by the U.S. government.

While it's unclear what the demands are, it's unlikely they will be met. The United States has a policy of refusing to pay ransoms to terrorists and rarely negotiates with them. Rescue missions like last week's are one of the few options left for the U.S. government when dealing with Americans being held hostage abroad. The big problem is that these rescues can be very difficult to pull off.

Another recent failed rescue sounds remarkably similar to the case in Yemen. As Adam Goldman and Karen DeYoung reported for The Washington Post back in August, several dozen U.S. commandos were sent to Syria last summer to try to rescue American hostages being held by the Islamic State. It was the first known U.S. ground operation in Syria since the country’s civil war started. An official told The Post that the effort “was not ultimately successful because the hostages were not present . . . at the site of the operation.” The operation was only revealed after video was released of the killing of James Foley, one of the Americans who was being held.

Both the rescue operation in Yemen and the one in Syria apparently failed due to problems with the intelligence used to plan the raids, a recurring issue for rescue teams in hostile foreign environments. Another big problem is that it can be hard to protect the hostages while fighting their captors: Linda Norgrove, a Scottish aid worker kidnapped by the Taliban in 2010, was killed during the U.S. operation to rescue her. A joint investigation between the United Kingdom and the United States later concluded that a grenade thrown by a member of the rescue team had killed Norgrove. Even in successful raids, the rescuers may well end up dead themselves.

These rescue missions may well cost more than many ransom demands. "In terms of cost, this is almost going to be an impossible figure," Brian Michael Jenkins, a Senior Adviser to the Rand Corporation President and terrorism expert told The Post. "It will depend on exactly how you want to do the accounting." Jenkins said that estimates could range between hundreds of thousands in the minimum to tens of millions of dollars, though he cautioned that cost wasn't the issue. "It is not a matter of cost effectiveness," Jenkins says.

The United States is far from alone in finding hostage rescue attempts extremely difficult. In 2013, French commandos failed to rescue intelligence agent Denis Allex from his Somalian captors, and Allex was executed in response. A 2012 attempt to rescue a Briton and his Italian colleague from Nigeria's Boko Haram failed when their captors killed the hostages. Ultimately, hostage rescues are always going to be difficult. "There's a lot of luck involved in this," Peter Ahearn, a former FBI agent, said of the failed attempt to rescue Foley last summer. "But you'd rather be lucky than good in some of these things."

In popular culture, however, the successful hostage rescues are the ones that are well-known. Israelis are proud of the daring 1976 Operation Entebbe, which saw 102 hostages rescued in a Ugandan air field. The British love to talk about 1980s Iranian Embassy Siege in London, which saw all but one of the hostages being held rescued in front of live television cameras. Two of the biggest American films of the past few years, "Captain Philips" and "Argo," dealt with successful U.S. hostage rescues.

History is filled with failed attempts, too, however. The events depicted in "Argo" were quickly followed by one of the most notorious hostage rescue attempts ever: 1980's Operation Eagle Claw, a failed attempt to rescue diplomats being held in the U.S. Embassy in Tehran that ended in a helicopter crash in the desert that left eight troops dead. That was the first mission by the U.S. military’s Joint Special Operations Command, or JSOC, which often deals with hostages held by terror groups.

Tactics have surely improved since then. Jenkins of Rand Corporation says that in 1980, almost 80 percent of U.S. hostage rescues resulted in at least one hostage dying. In the past few years, a little more than half of U.S. attempts were successful. That's still a high number, but given that the United States refuses to negotiate with terrorists, and that most Americans support that policy, there may be no better option.

"If a country is going to adopt a no ransom policy," Jenkins says, it must be willing to "take every reasonable effort to bring about their release without making concessions, and that includes, when feasible, a rescue attempt."

Correction: This article originally stated that Operation Eagle Claw preceded the events shown in the film "Argo." It has been corrected.