Missile defense
Missile defense categories: Missile defense can be divided into categories based on various characteristics: type/range of missile intercepted, the trajectory phase where the intercept occurs, and whether intercepted inside or outside the Earth's atmosphere:

Type/range of missile intercepted: These types/ranges include strategic, theater and tactical. Each entails unique requirements for intercept; a defensive system capable of intercepting one missile type frequently cannot intercept others. However, there is sometimes overlap in capability.

Strategic: Targets long-range ICBMs, which travel at about 7 km/s (15,700 mph). Examples of currently active systems: Russian A-135, which defends Moscow, the US Ground-Based Midcourse Defense that defends the United States from missiles launched from Asia and the Israeli Arrow 3 which defends Israel from ICBMs. Geographic range of strategic defense can be regional (Russian system) or national (US and Israeli system's).

Theater: Targets medium-range missiles, which travel at about 3 km/s (6,700 mph) or less. In this context, the term "theater" means the entire localized region for military operations, typically a radius of several hundred kilometers; defense range of these systems is usually on this order. Examples of deployed theater missile defenses: Israeli Arrow 2 missile and David's Sling, American THAAD, and Russian S-400.

Tactical: Targets short-range tactical ballistic missiles, which usually travel at less than 1.5 km/s (3,400 mph). Tactical anti-ballistic missiles (ABMs) have short ranges, typically 20–80 km (12–50 miles). Examples of currently-deployed tactical ABMs:israeli Iron Dome, American MIM-104 Patriot and Russian S-300V.

Trajectory phase: Ballistic missiles can be intercepted in three regions of their trajectory: boost phase, midcourse phase, or terminal phase.

Boost phase: Intercepting the missile while its rocket motors are firing, usually over the launch territory.
Advantages:

Bright, hot rocket exhaust makes detection and targeting easier.
Decoys cannot be used during boost phase.
At this stage, the missile is full of flammable propellant, which makes it very vulnerable to explosive warheads.
Disadvantages:

Difficult to geographically position interceptors to intercept missiles in boost phase (not always possible without flying over hostile territory).
Short time for intercept (typically about 180 seconds).

Mid-course phase: Intercepting the missile in space after the rocket burns out (example: American Ground-Based Midcourse Defense (GMD), Chinese SC-19 & DN-series missiles, Israeli Arrow 3 missile).
Advantages:

Extended decision/intercept time (the coast period through space before reentering the atmosphere can be several minutes, up to 20 minutes for an ICBM).
Very large geographic defensive coverage; potentially continental.
Disadvantages:

Requires large, heavy anti-ballistic missiles and sophisticated powerful radar which must often be augmented by space-based sensors.
Must handle potential space-based decoys.

Terminal phase: Intercepting the missile after it reenters the atmosphere (examples: American Aegis Ballistic Missile Defense System, Chinese HQ-29, American THAAD, American Sprint, Russian ABM-3 Gazelle)
Advantages:

Smaller, lighter anti-ballistic missile is sufficient.
Balloon decoys do not work during reentry.
Smaller, less sophisticated radar required.
Disadvantages:

Very short intercept time, possibly less than 30 seconds.
Less defended geographic coverage.
Possible blanketing of target area with hazardous materials in the case of detonation of nuclear warhead(s).

Intercept location relative to the atmosphere: Missile defense can take place either inside (endoatmospheric) or outside (exoatmospheric) the Earth's atmosphere. The trajectory of most ballistic missiles takes them inside and outside the Earth's atmosphere, and they can be intercepted in either place. There are advantages and disadvantages to either intercept technique.
Some missiles such as THAAD can intercept both inside and outside the Earth's atmosphere, giving two intercept opportunities.

Endoatmospheric: Endoatmospheric anti-ballistic missiles are usually shorter ranged (e.g., American MIM-104 Patriot, Indian Advanced Air Defence).
Advantages:

Physically smaller and lighter
Easier to move and deploy
Endoatmospheric intercept means balloon-type decoys won't work
Disadvantages:

Limited range and defended area
Limited decision and tracking time for the incoming warhead

Exoatmospheric: Exoatmospheric anti-ballistic missiles are usually longer-ranged (e.g., American GMD, Ground-Based Midcourse Defense).
Advantages:

More decision and tracking time
Fewer missiles required for defense of a larger area
Disadvantages:

Larger and heavier missiles required
More difficult to transport and place compared to smaller missiles
Must handle decoys

Countermeasures to missile defense: Given the immense variety by which a defense system can operate (targeting nuclear-armed intercontinental ballistic missiles (ICBMs), tactical, and theater missiles), there are some unarguably effective exoatmospheric (outside the Earth's atmosphere) countermeasures an attacking party can use to deter or completely defend against certain types of defense systems, ranges of ACBM's, and intercept locations. Many of defenses to these countermeasures have been implemented and taken into account when constructing missile defense systems, however, it does not guarantee their effectiveness or success.  The US Missile Defense Agency has received scrutiny in regards to their lack of foresight of these countermeasures, causing many scientists to perform various studies and data analysis as to the true effectiveness of these countermeasures.

Decoys: A common countermeasure that attacking parties use to disrupt the efficacy of Missile Defense Systems are the simultaneous launching of decoys from the primary launch site or from the exterior of the main attacking missile itself. These decoys are usually small, lightweight dud rockets that take advantage of the interceptor sensors tracking and fool it by making many different targets available in an instant.  This is accomplished via the releasing of decoys in certain phases of flight. Because objects of differing weights follow the same trajectory when in space, decoys released during the midcourse phase can prevent interceptor missiles from accurately identifying the warhead. This could force the defense system to attempt to destroy all incoming projectiles, which masks the true attacking missile and lets it slip by the defense system.

Common types of decoys: Since there can be many forms of this type of deception of a missile system, different categorizations of decoys have developed, all of which operate and are designed slightly different. Details of these types of decoys and their effectiveness were provided in a report by a variety of prominent scientists in 2000.

Replica decoys: This categorization of decoy is the most similar to the standard understanding of what a missile decoy is. These types of decoys attempt to mask the attacking ICBM via the release of many similar missiles. This type of decoy confuses the missile defense system by the sudden replication and the sheer amount that the defense has to deal with. Knowing that no defense system is 100% reliable, this confusion within the targeting of the defense system would cause the system to target each decoy with equal priority and as if it was the actual warhead, allowing the real warheads chance of passing through the system and striking the target to increase drastically.

Decoys using signature diversity: Similar to replica decoys, these types of decoys also take advantage of the limitations in number within the missile defense systems targeting. However, rather than using missiles of similar build and trace to the attacking warhead, these types of decoys all have slightly different appearances from both each other and the warhead itself. This creates a different kind of confusion within the system; rather than creating a situation where each decoy (and the warhead itself) appears the same and is therefore targeted and treated exactly like the "real" warhead, the targeting system simply does not know what is the real threat and what is a decoy due to the mass amount of differing information. This creates a similar situation as the result of the replica decoy, increasing the chance that the real warhead passes through the system and strikes the target.

Decoys using antisimulation: This type of decoy is perhaps the most difficult and subversive for a missile defense system to determine. Instead of taking advantage of the missile defense system's targeting, this type of decoy intends to fool the operation of the system itself. Rather than using sheer quantity to overrun the targeting system, an anti-simulation decoy disguises the actual warhead as a decoy, and a decoy as the actual warhead. This system of "anti-simulation" allows the attacking warhead to, in some cases, take advantage of the "bulk-filtering" of certain missile defense systems, in which objects with characteristics of the warhead poorly matching those expected by the defense are either not observed because of sensor filters, or observed very briefly and immediately rejected without the need for a detailed examination. The actual warhead may simply pass by undetected, or rejected as a threat.

Cooled shrouds: Another common countermeasure used to fool missile defense systems are the implementation of cooled shrouds surrounding attacking missiles. This method covers the entire missile in a steel containment filled with liquid oxygen, nitrogen, or other sub-zero coolants that prevent the missile from being easily detected. Because many missile defense systems use infrared sensors to detect the heat traces of incoming missiles, this capsule of extremely cold liquid either renders the incoming missile entirely invisible to detection or reduces the system's ability to detect the incoming missile fast enough.

Other types of infrared stealth: Another commonly applied countermeasure to missile defense is the application of various low-emissivity coatings.