Some of the key factions and leaders of the insurgency in Afghanistan:
A militant organization comprised of top leadership of the Afghan Taliban, which has been based in Quetta, Pakistan, since 2001. Three of the four insurgent leaders said to be taking part in the current Kabul talks are from the Quetta Shura, according to news reports. The President's powerful half brother, Ahmed Wali Karzai, the leading political figure in Kandahar, has also claimed to be in parallel talks with figures from the Quetta Shura.
Mullah Mohammed Omar: The spiritual leader of the Taliban movement and leader of the Quetta Shura. He is believed to be in Pakistan orchestrating the Taliban insurgency in southern and western Afghanistan. He is, however, not part of the current round of discussions taking place in Kabul. The Karzai government and the West is hoping large parts of the insurgency will defect from Mullah Omar and join the government under certain conditions.
Mullah Abdul Ghani Barader: He served as Mullah Omar's deputy until his capture by U.S. and Pakistani forces in Pakistan in February, 2010. Mullah Barader was seen as the de facto leader of the Taliban and the Quetta Shura since 2009. He is considered more amenable to a negotiated settlement to the conflict and was believed to be in talks with the Karzai government when he was arrested. Pakistan reportedly released him from prison this week. He would presumably play a key role in any talks, though he is not believed to be at the table.
Based out of the Pakistani city of Peshawar, it's thought to be led by Taliban commander Abdul Latif Mansur, who replaced Maluvi Abdul Kabir, who is apparently in the custody of Pakistan's intelligence service. The Peshawar Shura directs the insurgency in eastern and northeastern Afghanistan. While it is apparently not present at the Kabul talks, it has apparently engaged with the Karzai government before. Ahmed Wali Karzai has also claimed to be in contact with leaders from the Peshawar Shura.
He leads the insurgency in several eastern provinces. His proxies have been in talks for several years with Mr. Karzai, but negotiations floundered. The former prime minister founded a party called Hezb-e-Islami, a faction of which already shares political power in Kabul. This faction is thought to be most likely to cut a deal with Mr. Karzai, but it is also the least significant because Mr. Hekmatyar's power is limited and he alone cannot halt the insurgency.
It's named after Jalaluddin Haqqani, a former minister in the Taliban government in the 1990s who now presides over a Mafia-like network based in North Waziristan, in the border regions with Pakistan. The Haqqani network has close ties to elements of al-Qaeda and Pakistan's intelligence service, the ISI. It represents the most hard-line element of the insurgency. Jalaluddin Haqqani, now 67, recently handed command over to his son Sirajuddin after falling ill. Sirajuddin has a significant influence over the insurgency in eastern Afghanistan and has orchestrated some of the most spectacular suicide attacks in major urban centres. One of the four insurgent leaders said to be taking part in the current Kabul talks is from the Haqqani network.