When her husband blew himself up in a luxury hotel during a wedding in Amman a decade ago, Sajida al-Rishawi was meant to die too, but her suicide bomb belt did not go off. Today, as a death-row prisoner in Jordan, she is a heroine to jihadis in the region, who may be willing to swap a Jordanian pilot for her.

Rishawi, now in her mid-40s, has an influential background in militant circles: she hails from a powerful Sunni clan in Western Iraq, and her brother was a top lieutenant of Abu Musab al-Zarqawi, the founder of al-Qaida's Iraq branch. Today, that group has since transformed itself into the Islamic State group, breaking off from al-Qaida and controlling swaths of Iraq and Syria.

One of her cousins, Abdul Sittar Abu Risha, was a major figure in establishing the Sunni Awakening, a tribal movement that joined forces with the U.S. military and turned against al-Qaida.