Short answers, pulled from the story.
James Fearon and David Laitin define insurgency as a technology of military conflict characterized by small, lightly armed bands practicing guerrilla warfare from rural base areas. Austin Long adds that insurgency involves the use of political and military means by irregular forces to change an existing political order, with those forces typically mingling with civilians to avoid detection.
Insurgency aims for political control rather than resorting to indiscriminate violence, whereas a purely terrorist group's violence replaces rather than complements a political program. Michael F. Morris, whose essay won the 24th Annual United States Chairman of the Joint Chiefs of Staff Strategic Essay Contest, noted that insurgencies normally field fighting forces orders of magnitude larger than terrorist organizations and often maintain a legal political wing alongside covert operations.
Eizenstat identifies a security gap, a capacity gap, and a legitimacy gap. The security gap occurs when a government cannot protect citizens from internal and external threats, as in Haiti, Nepal, and Somalia. The capacity gap involves failures in survival services such as water, food, and public health, and the legitimacy gap refers to governments that lack the consent of the governed or tolerate widespread corruption.
The Somali Civil War, particularly the period from 1998 to 2006, is a recognized example of a multipolar insurgency with no recognized authority, in which the country broke into quasi-autonomous smaller states fighting among one another in changing alliances. The Angolan Civil War also involved two main sides, MPLA and UNITA, alongside a separate separatist movement for the Cabinda region led by FLEC.
In the information-centric framework developed by Berman and Matanock, civilians are the central actors in asymmetric conflicts. Civilians can share local information anonymously with government forces, enabling those forces to effectively target rebels. Both governments and rebels therefore divert resources toward providing services to civilians in order to influence whether civilians share that information.
A study by Juan Camilo Bohorquez, Sean Gourley, Alexander R. Dixon, Michael Spagat, and Neil F. Johnson found a common statistical structure across nine contemporary insurgent wars, drawing on data from more than 50,000 insurgent attacks. The study identified a recurrent pattern in the distribution of deaths across insurgent and terrorist events, suggesting insurgencies across different contexts share underlying mathematical regularities.