Counterinsurgency
Models: Counterinsurgency is normally conducted as a combination of conventional military operations and other means, such as demoralization in the form of propaganda, Psy-ops, and assassinations. Counter-insurgency operations include many different facets: military, paramilitary, political, economic, psychological, and civic actions taken to defeat insurgency.
To understand counterinsurgency, one must understand insurgency to comprehend the dynamics of revolutionary warfare. Counter-insurgency focuses on bridging these gaps. Insurgents take advantage of social issues known as gaps. When the gaps are wide, they create a sea of discontent, creating the environment in which the insurgent can operate.
In The Insurgent Archipelago, John Mackinlay puts forward the concept of an evolution of the insurgency from the Maoist paradigm of the golden age of insurgency to the global insurgency of the start of the 21st century. He defines this distinction as "Maoist" and "post-Maoist" insurgency.

Counterinsurgency theorists: 

Santa Cruz de Marcenado: The third Marques of Santa Cruz de Marcenado (1684–1732) is probably the earliest author who dealt systematically in his writings with counterinsurgency. In his Reflexiones Militares, published between 1726 and 1730, he discussed how to spot early signs of an incipient insurgency, prevent insurgencies, and counter them, if they could not be warded off. Strikingly, Santa Cruz recognized that insurgencies are usually due to real grievances: "A state rarely rises up without the fault of its governors." Consequently, he advocated clemency towards the population and good governance, to seek the people's "heart and love".

B. H. Liddell Hart: Liddell Hart attributed the failure of counterinsurgencies to various causes. First, as pointed out in the Insurgency addendum to the second version of his book Strategy: The Indirect Approach, a popular insurgency has an inherent advantage over any occupying force. He showed as a prime example the French occupation of Spain during the Napoleonic wars. Whenever Spanish forces managed to constitute themselves into a regular fighting force, the superior French forces beat them every time.
However, once dispersed and decentralized, the irregular nature of the rebel campaigns proved a decisive counter to French superiority on the battlefield. Napoleon's army had no means of effectively combating the rebels, and in the end, their strength and morale were so sapped that when Wellington was finally able to challenge French forces in the field, the French had almost no choice but to abandon the situation.
Counterinsurgency efforts may be successful, especially when the insurgents are unpopular. The Philippine–American War, the Shining Path in Peru, and the Malayan Emergency have been the sites of failed insurgencies.
Hart also points to the experiences of T. E. Lawrence and the Arab Revolt during World War I as another example of the power of the rebel/insurgent. Though the Ottomans often had advantages in manpower of more than 100 to 1, the Arabs' ability to materialize out of the desert, strike, and disappear again often left the Turks reeling and paralyzed, creating an opportunity for regular British forces to sweep in and finish the Turkish forces off.
In both the preceding cases, the insurgents and rebel fighters were working in conjunction with or in a manner complementary to regular forces. Such was also the case with the French Resistance during World War II and the National Liberation Front during the Vietnam War. The strategy in these cases is for the irregular combatant to weaken and destabilize the enemy to such a degree that victory is easy or assured for the regular forces. However, in many modern rebellions, one does not see rebel fighters working in conjunction with regular forces. Rather, they are home-grown militias or imported fighters who have no unified goals or objectives save to expel the occupier.
According to Liddell Hart, there are few effective counter-measures to this strategy. So long as the insurgency maintains popular support, it will retain all of its strategic advantages of mobility, invisibility, and legitimacy in its own eyes and the eyes of the people. So long as this is the situation, an insurgency essentially cannot be defeated by regular forces.

David Galula: David Galula gained his practical experience in counterinsurgency as a French Army officer in the Algerian War. His theory of counterinsurgency is not primarily military, but a combination of military, political and social actions under the strong control of a single authority.
Galula proposes four "laws" for counterinsurgency:

The aim of the war is to gain the support of the population rather than control of territory.
Most of the population will be neutral in the conflict; support of the masses can be obtained with the help of an active friendly minority.
Support of the population may be lost. The population must be efficiently protected to allow it to cooperate without fear of retribution by the opposite party.
Order enforcement should be done progressively by removing or driving away armed opponents, then gaining the support of the population, and eventually strengthening positions by building infrastructure and setting long-term relationships with the population. This must be done area by area, using a pacified territory as a basis of operation to conquer a neighboring area.
Galula contends that:

A victory [in a counterinsurgency] is not the destruction in a given area of the insurgent's forces and his political organization. ... A victory is that plus the permanent isolation of the insurgent from the population, isolation not enforced upon the population, but maintained by and with the population. ... In conventional warfare, strength is assessed according to military or other tangible criteria, such as the number of divisions, the position they hold, the industrial resources, etc. In revolutionary warfare, strength must be assessed by the extent of support from the population as measured in terms of political organization at the grassroots. The counterinsurgent reaches a position of strength when his power is embedded in a political organization issuing from, and firmly supported by, the population.
With his four principles in mind, Galula goes on to describe a general military and political strategy to put them into operation in an area that is under full insurgent control:

In a Selected Area
1. Concentrate enough armed forces to destroy or to expel the main body of armed insurgents.
2. Detach for the area sufficient troops to oppose an insurgent come back in strength, install these troops in the hamlets, villages, and towns where the population lives.
3. Establish contact with the population, control its movements in order to cut off its links with the guerrillas.
4. Destroy the local insurgent political organization.
5. Set up, by means of elections, new provisional local authorities.
6. Test those authorities by assigning them various concrete tasks. Replace the softs and the incompetents, give full support to the active leaders. Organize self-defense units.
7. Group and educate the leaders in a national political movement.

8. Win over or suppress the last insurgent remnants.
According to Galula, some of these steps can be skipped in areas that are only partially under insurgent control, and most of them are unnecessary in areas already controlled by the government. Thus the essence of counterinsurgency warfare is summed up by Galula as "Build (or rebuild) a political machine from the population upward."

Robert Thompson: Robert Grainger Ker Thompson wrote Defeating Communist Insurgency in 1966, wherein he argued that a successful counterinsurgency effort must be proactive in seizing the initiative from insurgents. Thompson outlines five basic principles for a successful counterinsurgency:

The government must have a clear political aim: to establish and maintain a free, independent and united country that is politically and economically stable and viable;
The government must function in accordance with the law;
The government must have an overall plan;
The government must give priority to defeating political subversion, not the guerrilla fighters;
In the guerrilla phase of an insurgency, a government must secure its base areas first.

David Kilcullen: In "The Three Pillars of Counterinsurgency", Dr. David Kilcullen, the Chief Strategist of the Office of the Coordinator for Counterterrorism of the U.S. State Department in 2006, described a framework for interagency cooperation in counterinsurgency operations. His pillars – Security, Political and Economic – support the overarching goal of Control, but are based on Information:

This is because perception is crucial in developing control and influence over population groups. Substantive security, political and economic measures are critical but to be effective they must rest upon, and integrate with a broader information strategy. Every action in counterinsurgency sends a message; the purpose of the information campaign is to consolidate and unify this message. ... Importantly, the information campaign has to be conducted at a global, regional and local level — because modern insurgents draw upon global networks of sympathy, support, funding and recruitment.
Kilcullen considers the three pillars to be of equal importance because

unless they are developed in parallel, the campaign becomes unbalanced: too much economic assistance with inadequate security, for example, simply creates an array of soft targets for the insurgents. Similarly, too much security assistance without political consensus or governance simply creates more capable armed groups. In developing each pillar, we measure progress by gauging effectiveness (capability and capacity) and legitimacy (the degree to which the population accepts that government actions are in its interest).