Today in Algeria, authorities are scouring a Saharan gas plant for bodies in the wake of a hostage crisis that ended in a shootout between the Army and Islamist kidnappers. Around the world, leaders are vowing to strike back hard at Islamist militancy that is surging across North Africa.

Meanwhile, in neighboring Mali, France is already leading a military intervention to dislodge Islamist fighters who seized the country's north last year. Paris has pledged to keep its troops there until those fighters are defeated and Mali is returned to stability.

So what are Western governments and their North African partners up against? It's a murky picture, but here are some outlines:

Is this a regional problem?

Yes. North Africa is home to various armed groups, from ideologically driven Islamists to criminal gangs. While their aims and loyalties don’t always overlap, they have shown an increasing inclination to work together. Some have international appeal, with members reportedly hailing from a range of countries. And many operate across national borders, which count for little in the deep Sahara.

Could the problem get worse?

Yes. If unchecked, violence could intensify, at least in North African countries. Hardline Islamist ideology has gathered steam chiefly among poor young men left adrift amid youth unemployment and lack of development. Deepening conflict could also affect oil markets if installations in Algeria or Libya – both major hydrocarbons producers – come under threat.

Where does North African militancy come from?

Much Islamist militancy in North Africa traces its origins to 1990s Algeria, when the Army’s decision to cancel elections that an Islamist party was expect to win tipped the country into a decade of civil strife. Tens of thousands were killed in bombings, massacres, and disappearances, as government forces battled Islamist insurgents led by veterans of the Afghan war of the 1980s.

While Algeria is largely stable today, a militant Islamist faction called the Salafist Group for Call and Combat has continued attacks mainly on government forces. In 2007 the group formally changed its name to Al Qaeda in the Islamic Maghreb (AQIM) and remains North Africa’s premier militant Islamist outfit.

Who’s out there?

AQIM is North Africa’s most powerful Islamist militant group, operating mainly in Algeria and northern Mali. While its exact structure isn’t clear, it seems to consist of a northern wing based in Algeria’s Kabylie region and Saharan bands based in northern Mali.

Also in Mali are Ansar al Din and the Movement for Unity and Jihad in West Africa (MUJAO). With AQIM, these groups have seized control of Mali’s north. Their numbers are hard to gauge, but are believed to range in the hundreds to thousands.

Elsewhere in North Africa, small apparently independent groups – sometimes just a dozen or so people – have staged occasional bombings in recent years (Morocco) and gotten into firefights with police (Tunisia).

What do militants believe?

Most Islamist militants appear to share a brand of violent Salafism forged largely in the crucible of the 1980s Afghan war. Broadly, Salafis believe Islam should be followed to the letter in a quest to emulate the first generations of Muslims. That means rejecting centuries of Islamic thought and scholarship that most Muslims see as integral to their faith and worship. While many Salafis don’t espouse violence, a minority – including North Africa’s militants – do.

What do they want?

It’s often hard to say exactly. In general, Islamist militants want to apply their religious beliefs, something that involves imposing their brand of Islam on other people. In northern Mali, militants have set up a harsh rule that includes amputating the hands of alleged thieves, banning music, and stoning people accused of adultery. However, some groups have also stated more specific political aims. AQIM, for example, has long said it wants to set up an Islamic state in Algeria.

Do they work together?

Sometimes. Northern Mali is one example, where Ansar al Din, MUJAO, and AQIM are holding the north in concert with each other. Reports of black English-speakers among the ranks of the MUJAO also suggest that members of Boko Haram – Islamist militants from northern Nigeria – may at least be moonlighting as members of the Malian group.

More fundamentally, militant groups show solidarity. Last week’s kidnappers in Algeria claimed their attack was retribution for the French-led intervention in Mali, and demanded it be stopped. While security analysts say the attack was probably planned before France took action, it still offered perpetrators a chance to give fellow Islamists a hand.

What do other Muslims in North Africa think?

Nearly all reject utterly the violence and harsh ideology of Islamist militants, of which they are the principal victims. Indeed, the practice by some militant groups of takfir - branding a fellow Muslim a kafir, or unbeliever – is considered a sin in mainstream Islam.

What have governments done so far to combat them?

Responses have varied. Some have waged military campaigns, while others have focused on police work. Western allies have offered assistance, to mixed effect.

Algeria won peace with a 2005 amnesty for militants who laid down their arms. The Army continues to fight AQIM, however. Algeria has also taken the lead in recent years in rallying North and West African governments to cooperate on security. Given this, last week’s debacle – a rare attack on an oil installation – has shocked observers.

The US has spent millions of dollars on counterterrorism training for armies including those of Algeria and Mali. The swift collapse of Mali’s Army last year left observers wondering what went wrong.

Where do militants get money?

Details are murky. Governments and security experts all say the AQIM – and perhaps other groups – are plugged into drug-smuggling networks, most likely selling protection or simply taxing the smugglers. Kidnappings are also a main source of cash. AQIM in particular has reportedly raked in millions of euros from European governments in return for releasing their citizens. (Governments routinely deny that ransoms have been paid.)

Has the Arab Spring changed the game?

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Yes. The revolutions in Tunisia and Libya in 2011 threw security services off balance, allowing militants to move more freely in those countries and across their borders. In Libya, Muammar Qaddafi’s vast arsenals were looted, with weapons from small arms to thousands of surface-to-air missiles pouring onto the black market.

More fundamentally, the fall of dictators opened Tunisia's and Libya's societies – for better and for worse. In both countries, Salafi minorities have asserted themselves, sometimes violently. The starkest examples to date are arguably attacks on US diplomatic facilities last September.