Combined arms
During the evening meal the French were surprised by an attack under the cover of English archers. The disorganized French forces were slaughtered and had no choice but to withdraw.

15th to 18th centuries: Generally the savanna cavalries of West Africa used a combined arms approach, seldom operating without supporting infantry.
The French army of the Valois kings, composed of heavily armoured gendarmes (professional versions of the medieval knight), Swiss and Landsknecht mercenary pikemen, and heavy cannons took form during the transition from the medieval way of war to the early modern period.
The late 15th century saw the development of combined pike and shot formations in Europe, starting with the colunelas of the Spanish general Gonzalo Fernández de Córdoba, evolving into the tercios of Hapsburg Spain and the Imperial Army of the Holy Roman Empire during the 16th century.
In Japan, at the battle of Nagashino (長篠の戦い) in 1575, forces of the Oda clan successfully employed combined arms against the Takeda clan, which heavily relied on cavalry. The Oda army erected palisades to protect their ashigaru musketeers that shot down the Takeda cavalry while their samurai cut down any enemies who managed to approach melee range.
The 17th century saw increasing use of combined arms at lower (regimental) level. King Gustavus Adolphus of Sweden was the proponent of the idea. For fire support he attached teams of "commanded musketeers" to cavalry units and fielded light 3-pounder guns to provide infantry units with organic artillery.
In the eighteenth century, the concept of the legion was revived. Legions now consisted of musketeers, light infantry, dragoons and artillery in a brigade sized force. These legions often combined professional military personnel with militia. Perhaps the most notable example is the use of light cavalry, light infantry and light horse artillery in advance detachments by France's La Grande Armée during the Napoleonic Wars.

Napoleonic Wars: After 25 years of near continuous warfare, the armies that met at the Battle of Waterloo in 1815 were organized in a similar manner – into corps which contained infantry, cavalry and artillery (see Order of battle of the Waterloo Campaign), and used similar combined arms tactics. Within each corps were divisions of infantry or cavalry made up of brigades and an artillery unit. An army would usually also have reserves of all three arms under the direct command of the army commander which could be sent in support of any corps or division of a corps to increase any arm which the army general considered necessary. The great French cavalry charge commanded by Marshal Ney during the battle failed to break Wellington's squares of infantry and Ney's failure to supplement his cavalry with sufficient horse artillery to break the squares open is usually given as a major contributing factor in the failure. It is an example of why generals needed to use combined arms to overcome the tactics used by enemy officers to frustrate an attack by a single arm of an army.
In contrast the 27th (Inniskilling) suffered 478 casualties from an initial strength of 750 because of their exposure to attack by French combined arms. They were located near the centre of Wellington's line, but unlike most of the rest of Wellington's infantry were in a declivity on the exposed side of the Mont-Saint-Jean escarpment. Exposed as they were, they were forced to stand in square for most of the day for fear of cavalry attack and so made an easy dense target for Napoleon's massed artillery.

20th-century developments: 

First World War: The development of modern combined arms tactics began in the First World War. Early in the Western Front, fighting descended into stagnant trench warfare. Generals on both sides applied conventional military thinking to the new weapons and situations that they faced. In these early stages, tactics typically consisted of heavy artillery barrages followed by massed frontal assaults against well entrenched enemies. These tactics were largely unsuccessful and resulted in large loss of life.
As the war progressed new combined arms tactics were developed, often described then as the "all arms battle". These included direct close artillery fire support for attacking soldiers (the creeping barrage), air support and mutual support of tanks and infantry. One of the first instances of combined arms was the Battle of Cambrai, in which the British used tanks, artillery, infantry, small arms and air power to break through enemy lines. Previously such a battle would have lasted months with many hundreds of thousands of casualties. Co-ordination and planning were the key elements, and the use of combined arms tactics in the Hundred Days Offensive in 1918 allowed the Allied forces to exploit breakthroughs in the enemy trenches, forcing the surrender of the Central Powers.

Second World War: In World War II combined arms was a fundamental part of some operational doctrines like Heinz Guderian's Blitzkrieg, or the Soviet deep battle doctrine, which was based on combining tanks, mobile units (mechanised infantry or cavalry) and infantry, while supported by artillery.

Cold War years: In 1963 the United States Marine Corps formalized the concept of the Marine Air-Ground Task Force, which combined Marine aviation and Marine ground units for expeditionary missions.
The Vietnam War had a profound influence on the development of the US Army's combined arms doctrine. Due to the very difficult terrain that prevented access to the enemy-held areas of operation, troops were often deployed by air assault. For this reason, US troops in Vietnam saw six times more combat than in preceding wars, due to less time spent on logistic delays. The result: an infantry unit increased in effectiveness by a factor of four for its size, when supported with helicopter-delivered ammunition, food and fuel. In time the US Army in Vietnam also learned to combine helicopter operations and airmobile infantry with the armoured and artillery units operating from fire support bases as well as the US brown-water navy and USAF close air support units supporting them.
AirLand Battle was the overall conceptual framework that formed the basis of the US Army's European warfighting doctrine from 1982 into the late 1990s. AirLand Battle emphasized close coordination between land forces acting as an aggressively maneuvering defense, and air forces attacking rear-echelon forces feeding those front line enemy forces.
In the 1991 Gulf War, General Schwarzkopf used a mix of strikes by fixed-wing aircraft including carpet bombing and precision bombing in combination with large numbers of strikes by attack helicopters. During the ground assault phase, tanks and other armoured fighting vehicles supported by attack aircraft swept over remaining forces. The front line moved forward at upwards of 40–50 km/h at the upper limit of the Army's tracked vehicles.

Post Cold War (1992–present): In 2000, the US Army began developing a new set of doctrines intended to use information superiority to wage warfare. Six pieces of equipment were crucial for this: AWACS (for Airborne early warning and control), JSTARS (for Airborne ground surveillance), GPS, VHF SINCGARS (for ground and airborne communications), and ruggedized computers. The mix is supplemented by satellite photos and passive reception of enemy radio emissions, forward observers with digital target designation, specialized scouting aircraft, anti-artillery radars and gun-laying software for artillery.
Based on this doctrine, many US ground vehicles moved across the landscape alone. If they encountered an enemy troop or vehicle concentration, they would assume a defensive posture, lay down as much covering fire as they could, designate the targets for requested air and artillery assets. Within a few minutes, on station aircraft would direct their missions to cover the ground vehicle. Within a half-hour heavy attack forces would concentrate to relieve the isolated vehicle. In an hour and a half the relieved vehicle would be resupplied.

See also: Joint warfare
Battlegroup (army)
Organic unit
Network-centric warfare
Maneuver warfare

References: 

Bibliography: Thornton, John Kelly (1999). Warfare in Atlantic Africa, 1500–1800. Routledge. ISBN 1857283937

Further reading: House, Jonathan M. (1984). "Toward Combined Arms Warfare: A survey of 20th-century tactics, doctrine, and organization". University Press of the Pacific. US Army Command General Staff College.
Perry, Roland (2004). Monash: The Outsider Who Won a War. Sydney: Random House.