Pakistan is broadening its offensive against the militants
For much of the last decade Nato forces in Afghanistan and Pakistani troops in the north-west of their country have been fighting Taliban and al-Qaeda militants.
So why is there conflict in the two countries and is there a link?
A US-led coalition spearheaded the invasion of Afghanistan in October 2001 because it said that the country was being used as a sanctuary by al-Qaeda leader Osama Bin Laden following the 9/11 attacks in the US.
From the outset, it has sought the help of Pakistan in rooting out insurgents, determined that there should be no safe havens for militants.
When it became clear that neither Bin Laden nor Taliban leader Mullah Omar had been killed or captured, the pressure on Pakistan to eject militants from its border areas increased.
Since then the Pakistani army has launched offensives against militant positions interspersed with controversial peace deals. The Americans in particular opposed these, arguing that they allowed the militants to re-group.
The latest such offensive began at the end of 2008, following the election of President Asif Ali Zardari. Pakistan is now pursuing militants across the north-west of the country.
Should the world be worried?
There is a near-universal consensus on this - and the answer is a resounding yes.
The principal concern is the security of Pakistan's nuclear weapons which it is feared could fall into Taliban or al-Qaeda hands.
The Taliban have proved themselves to be formidable adversaries
Most commentators agree that the possibility of this happening is remote, but concern still runs high.
In April 2009 US Secretary of State Hillary Clinton told a US Senate committee that while a lot of time was spent worrying about Iran getting nuclear weapons, Pakistan already had them.
Some feel the danger is being exaggerated in Washington in order to build support for the Obama administration's "Af-Pak policy".
But the BBC's Mark Urban says that the real danger lies in subversion - one or more individuals working inside the system providing militants with nuclear materials or even an entire atomic weapon.
There are concerns that India may become involved in the conflict against militancy - especially in Pakistan - if there is a repeat of the November 2008 Mumbai attacks, which were blamed on extremists operating out of Pakistan.
Both India and the US suspect that radical madrasas in Pakistan are exporting militants around the world.
What's being done to fight the militants?
Apart from the ongoing Pakistani army offensive in parts of the North West Frontier Province (NWFP) - where the Swat Valley was captured in the summer of 2009 - and in the Federally Administered Tribal Areas (Fata) the Americans have over the last few years used controversial drone attacks to hit militant targets in Pakistan from Afghanistan.
Nato says it aims to help stabilise Afghanistan
These have generated much concern because in many cases civilians have been killed in these attacks.
President Obama sent around 21,000 additional US troops to Afghanistan - and is reported to be looking at further considerable deployments.
Nato's commander in Afghanistan Gen Stanley McChrystal put the number of reinforcements needed at 40,000.
The commander has also stressed that if the war in Afghanistan is to be won, the development battle is almost as important as the military conflict - and that the protection of civilians must be put at the heart of the Afghan strategy.
The West has poured billions of dollars into north-west Pakistan and into Afghanistan for the construction of schools, hospitals and community centres.
How serious is Pakistan in defeating the Taliban?
Pakistan's government says that it is serious about tackling the Taliban. The country's powerful military is currently shoulder-to-shoulder with the government on this issue.
The former leader of the Taliban, Baitullah Mehsud, was killed in August 2009 by a US missile.
In October the army launched an offensive against Taliban militants loyal to his successor, Hakimullah Mehsud, based in South Waziristan.
It is Mehsud's fighters who are said to be behind recent attacks on military installations and personnel across the north-west of Pakistan. They have also been blamed for the string of suicide bombings which hit north-western Pakistan in October 2009.
But doubts remain over the army's willingness to fight those Taliban involved in cross-border attacks in Afghanistan. Indeed, some elements are thought to actively support militants fighting in Afghanistan.
They see seen as a useful counterweight to what the army says is the growing influence of perennial rival India in Central Asia.
So can Pakistan beat the militants?
At the moment that is difficult to say.
So far the militants appear to have been ejected from most of NWFP - including the Swat valley - but they are still entrenched in tribal areas.
Even if Pakistan does remove the militants from their strongholds in South Waziristan, many say the real challenge is in ensuring the Taliban does not get a foothold there again.
The terrain there is difficult and ideally suited to guerrilla warfare. No-one is expecting either the Taliban or al-Qaeda to disappear overnight.
What is the human cost in both countries?
The human cost of the war in both countries has been immense.
More than 100,000 people have left South Waziristan in anticipation of fighting there.
In Afghanistan, the UN says that there has been a sharp increase in the number of civilians killed compared to 2008.
The UN says that from January to August 1,445 civilians were killed - a rise of 39% on the same period last year.
Who is going to win overall?
In the short term, neither side in either country, are likely to claim victory.
Helmand is the 'largest single source of opium' in Afghanistan
Recent analysis of where things stand in Afghanistan was provided in June 2009 by Nato's outgoing supreme commander, Gen John Craddock.
He said that a lack of troops is putting severe constraints on its military operations in Afghanistan and that there was in effect a stalemate in the south and east of the country, the areas worst affected by the insurgency.
Nato commanders hope that President Obama will eventually send more troops to rectify this once the outcome of the Afghan presidential run-off vote is known.
In Pakistan, the army continues with its Waziristan offensive - but this is restricted to certain areas and certain groups in the region.
No-one expects them to be easily defeated in their mountainous homeland.