Military camouflage
Hugh Cott's 1940 book Adaptive Coloration in Animals systematically covered the different forms of camouflage and mimicry by which animals protect themselves, and explicitly drew comparisons throughout with military camouflage:

The principle is one with many applications to modern warfare. In the Great War it was utilized by the Germans when they introduced strongly marked incidents of white or black tone to conceal the fainter contrasts of tone made by the sloping sides of overhead camouflage-screens, or roofing, as seen from the air. The same principle has, of course, a special application in any attempt to reduce the visibility of large objects of all kinds, such as ships, tanks, buildings, and aerodromes.
Both British and Soviet aircraft were given wave-type camouflage paintwork for their upper surfaces throughout the war, while American ones remained simple two-colour schemes (different upper and under sides) or even dispensed with camouflage altogether. Italian and some Japanese aircraft wore sprayed-on spotted patterns. German aircraft mostly used an angular splint-pattern camouflage, but Germany experimented with different schemes, particularly in the later stages of the war. They also experimented with various spray-on camouflage patterns for tanks and other vehicles, while Allied vehicles remained largely uni-coloured. As they had volunteered in the first World War, women sewed camouflage netting, organizing formalized groups for the work in Australia, Britain, New Zealand and the United States who took part as camoufleurs during the second war.

The British Middle East Command Camouflage Directorate, consisting mainly of artists recruited into the Royal Engineers, developed the use of camouflage for large-scale military deception. Operations combined the disguise of actual installations, vehicles and stores with the simultaneous display of dummies, whether to draw fire or to give a false idea of the strength of forces or likely attack directions. In Operation Bertram for the decisive battle at El Alamein, a whole dummy armoured division was constructed, while real tanks were disguised as soft-skinned transport using "Sunshield" covers. The capabilities so developed were put to use not only in the western desert, but also in Europe as in the Operation Bodyguard deception for the Invasion of Normandy, and in the Pacific campaign, as in the Battle of Goodenough Island.
The introduction of strategic bombing led to efforts to camouflage airfields and strategic production centres. This form of positional camouflage could be quite elaborate, and even include false houses and cars. With the threat from nuclear weapons in the post-war era such elaborate camouflage was no longer seen as useful, as a direct hit would not be necessary with strategic nuclear weapons to destroy infrastructure. The Soviet Union's doctrine of military deception defines the need for surprise through means including camouflage, based on experiences such as the Battle of Kursk where camouflage helped the Red Army to overwhelm a powerful enemy.

Application: 

Uniforms: The role of uniform is not only to hide each soldier, but also to identify friend from foe. Issue of the "Frogskin" uniforms to US troops in Europe during the Second World War was halted as it was too often mistaken for the disruptively patterned German uniform worn by the Waffen-SS. Camouflage uniforms need to be made and distributed to a large number of soldiers. The design of camouflage uniforms therefore involves a tradeoff between camouflaging effect, recognizability, cost, and manufacturability.
Armies facing service in different theatres may need several different camouflage uniforms. Separate issues of temperate/jungle and desert camouflage uniforms are common. Patterns can to some extent be adapted to different terrains by adding means of fastening pieces of vegetation to the uniform. Helmets often have netting covers; some jackets have small loops for the same purpose. Being able to find appropriate camouflage vegetation or in other ways modify the issued battle uniform to suit the local terrain is an important skill for infantry soldiers.
Countries in boreal climates often need snow camouflage, either by having reversible uniforms or simple overgarments.

Land vehicles: The purpose of vehicle and equipment camouflage differs from personal camouflage in that the primary threat is aerial reconnaissance. The goal is to disrupt the characteristic shape of the vehicle, to reduce shine, and to make the vehicle difficult to identify even if it is spotted.
Paint is the least effective measure, but forms a basis for other techniques. Military vehicles often become so dirty that pattern-painted camouflage is not visible, and although matte colours reduce shine, a wet vehicle can still be shiny, especially when viewed from above. Patterns are designed to make it more difficult to interpret shadows and shapes. The British Army adopted a disruptive scheme for vehicles operating in the stony desert of the North African Campaign and Greece, retrospectively known as the Caunter scheme. It used up to six colours applied with straight lines.

The British Army's Special Air Service used pink as the primary colour on its desert-camouflaged Land Rover Series IIA patrol vehicles, nicknamed Pink Panthers; the colour had been observed to be indistinguishable from sand at a distance.
Nets can be effective at defeating visual observation. Traditional camouflage nets use a textile 'garnish' to generate an apparent texture with a depth of shadow created beneath it, and the effect can be reinforced with pieces of vegetation. Modern nets tend to be made of a continuous woven material, which is easier to deploy over a vehicle and lack the "windows" between patches of garnish of traditional nets. Some nets can remain in place while vehicles move. Simple nets are less effective in defeating radar and thermal sensors. Heavier, more durable "mobile camouflage systems", essentially conformal duvets with thermal and radar properties, provide a degree of concealment without the delay caused by having to spread nets around a vehicle.
Active camouflage for vehicles, using heated or cooled Peltier plates to match the infrared background, has been prototyped in industry but has not yet been put into production.

Ships: Until the 20th century, naval weapons had a short range, so camouflage was unimportant for ships, and for the men on board them. Paint schemes were selected on the basis of ease of maintenance or aesthetics, typically buff upperworks (with polished brass fittings) and white or black hulls. Around the start of the 20th century, the increasing range of naval engagements, as demonstrated by the Battle of Tsushima, prompted the introduction of the first camouflage, in the form of some solid shade of gray overall, in the hope that ships would fade into the mist.

First and Second World War dazzle camouflage, pioneered by English artist Norman Wilkinson, was used not to make ships disappear, but to make them seem smaller or faster, to encourage misidentification by an enemy, and to make the ships harder to hit. In the Second World War, the Royal Canadian Navy trialled a form of active camouflage, counter-illumination, using diffused lighting to prevent ships from appearing as dark shapes against a brighter sky during the night. It reduced visibility by up to 70%, but was unreliable and never went into production.
After the Second World War, the use of radar made camouflage generally less effective. However, camouflage may have helped to protect US warships from Vietnamese shore batteries using optical rangefinders.
Coastal patrol boats such as those of the Norwegian, Swedish and Indonesian navies continue to use terrestrial style disruptively patterned camouflage.

Aircraft: Aircraft camouflage faces the challenge that an aircraft's background varies widely, according to whether the observer is above or below the aircraft, and with the background, e.g. farmland or desert. Aircraft camouflage schemes have often consisted of a light colour underneath and darker colours above.
Other camouflage schemes acknowledge that aircraft may be seen at any angle and against any background while in combat, so aircraft are painted all over with a disruptive pattern or a neutral colour such as gray.

Second World War maritime patrol aircraft such as the Consolidated PBY Catalina flying boat were painted white, as aircraft generally appear dark against the sky (including at night), and hence are least visible when painted in as light a colour as possible. The problem of appearing dark against the sky was explored in the U.S. Navy's Yehudi lights project in 1943, using counter-illumination to raise the average brightness of a plane, when seen head-on, from a dark shape to the same as the sky. The experiments worked, enabling an aircraft to approach to within 2 miles (3.2 km) before being seen, whereas aircraft without the lights were noticed 12 miles (19 km) away.
The higher speeds of modern aircraft, and the reliance on radar and missiles in air combat have reduced the value of visual camouflage, while increasing the value of electronic "stealth" measures. Modern paint is designed to absorb electromagnetic radiation used by radar, reducing the signature of the aircraft, and to limit the emission of infrared light used by heat seeking missiles to detect their target. Further advances in aircraft camouflage are being investigated in the field of active camouflage.

In fashion and art: 

Fashion and the "Dazzle Ball": The transfer of camouflage patterns from battle to exclusively civilian uses is not recent. Dazzle camouflage inspired a trend of dazzlesque patterns used on clothing in England, starting in 1919 with the "Dazzle Ball" held by Chelsea Arts Club. Those attending wore dazzle-patterned black and white clothing, influencing twentieth-century fashion and art via postcards (see illustration) and magazine articles. The Illustrated London News announced

The scheme of decoration for the great fancy dress ball given by the Chelsea Arts Club at the Albert Hall, the other day, was based on the principles of 'Dazzle', the method of 'camouflage' used during the war in the painting of ships ... The total effect was brilliant and fantastic.