What has happened?
Authorities in the southern Philippines announced this week that they had found the decapitated head of a Canadian tourist, John Ridsdel, who had been taken hostage last year by Islamist guerrillas.
How long was he a hostage?
In September, Ridsdel, a 68-year-old former mining executive from Calgary, Alberta, was seized while on holiday near the city of Davao, on the island of Mindanao, by militants linked to the radical Abu Sayyaf group. He was taken with three others - a Norwegian man, another Canadian national and his Philippine girlfriend.
Why was he killed?
In video messages, the militants demanded US$80 million for the hostages' release, with a deadline set for April 25. Both Canada and the Philippines have explicit policies against the payment of ransoms, and the deadline passed.
The grisly evidence of Ridsdel's execution was dropped off in a plastic bag on a street in Jolo, capital of Sulu province, a long-standing cradle of Islamist militancy off the southwest coast of Mindanao.
What is the Philippines' Government doing?
The Government in Manila ordered the country's military and police to aggressively search for and rescue the remaining captives. "The intensified operations are ongoing. We have forces on the ground currently pursuing these bandits," army spokesman Restituto Padilla said.
What is the background to the insurgency?
Although it is a majority-Catholic nation, the Philippines still has a significant Muslim population, accounting for about 5 per cent of the country's almost 100 million people. Muslim sultanates held sway through much of the archipelago nation, particularly in the south, until the arrival of the Spanish in the 16th century. The Islam practiced there, like other faiths in Southeast Asia, is suffused with older indigenous beliefs, including the worship of local spirits.
The majority of the country's Muslims are now concentrated in Mindanao and adjacent islands. For decades, various separatist insurgencies have raged in the region; most of the groups are motivated more by political grievances and criminal opportunism than ideology.
When did Abu Sayyaf emerge?
In the early 1990s Abu Sayyaf became a radical splinter group of the Moro Islamic Liberation Front, a rebel faction that wants greater Muslim autonomy in the southern Philippines. Abu Sayyaf's leadership, which was said to have ties with al-Qaeda, aimed to forge its own Islamic state. The group went about emulating the Middle Eastern terrorist organisation.
What did it do?
It kidnapped 20 people from a resort in 2001, including three Americans, one of whom was beheaded. In 2004, Abu Sayyaf carried out the worst terrorist attack in the history of the Philippines, targeting a ferry in Manila Bay, leaving 116 people dead. The following year, its militants carried out bombings across the country.
How did the Government react?
The group has been largely subdued since Manila launched an intense counterinsurgency effort backed by US Special Operations forces. But it has not been defeated. A clash this month with state security forces led to the deaths of 18 soldiers.
How many hostages does it hold?
Various cells hold at least 19 hostages, including tourists, as well as Malaysian and Indonesian workers. Current estimates suggest that there are fewer than 400 fighters in Abu Sayyaf's ranks, a significant dip from its heyday in the 1990s. Moreover, there is no evidence that Abu Sayyaf receives any material support from al-Qaeda.
Does it still back al-Qaeda?
What has alarmed international observers were the apparent declarations of fealty to Isis (Islamic State) made by elements of Abu Sayyaf this year, including one by the group's titular head, Isnilon Hapilon, who has now styled himself Sheik Mujahid Abu Abdullah al-Filipini.
How much influence does Isis hold in the region?
The spectre of a transnational terrorist threat is a concern to many countries in the region. Hundreds of Southeast Asian extremists have joined Isis' ranks in Syria and Iraq. And suspected Indonesian proxies of the group carried out a deadly assault in central Jakarta in January.
What can be done?
Indonesian President Joko Widodo called for joint maritime patrols with Malaysia and the Philippines to better combat Abu Sayyaf and other militant groups operating in islands and communities far from the reach of all three nations' capitals. "We can't let this continue," the Indonesian leader declared.
What do experts believe?
Some experts believe that the key to quieting the insurgency in the Philippines is extending the rule of law and pushing through a peace process with other militant groups that are already in talks with Manila. Progress has stalled ahead of the country's presidential election, scheduled for May.
"Abu Sayyaf was formerly what we all think of when we think of a terrorist organisation," Greg Poling, director of the Asia Maritime Transparency Initiative, told CNN. But times have changed, he adds: "This is basically a group of criminals whose only support comes from family connections in the local communities."