Armoured warfare
These ideas culminated in the "PU-36" or the 1936 Field Service Regulations.

Wartime: At the start of the Second World War much of the Red Army, including its armoured forces, was in transition and recovering from the 1937 repression of the officer corps. The Red Army ignored the lessons from Nomonhan, which had been successfully conducted by General Zhukov, and relied instead on lessons from politically selected officers who were veterans of the Spanish Civil War. The result was a poor showing during the Winter War. The Red Army tank fleet was extremely large, consisting of some 24,000 vehicles, but many were obsolete or unfit for service due to difficulties with supplying spare parts and lack of qualified support staff.
One important development took place shortly before the war, which influenced Soviet armoured doctrine and tank design for a decade: the creation of the T-34. Developed on the Christie suspension chassis and using sloped armour for the first time, the T-34 proved a shock to the German forces in the first German encounter of Soviet T-34 and KV tanks. The T-34 had an excellent combination of mobility, protection and firepower.  Using wide tracks, the T-34 was also able to negotiate terrain in difficult weather conditions, something that persistently dogged the German designs. 
Assessing the success of the German Blitzkrieg strategy, operational methods and tactics, the Red Army concluded that it should return to the use of operational methods developed before the war, so the Tank Armies were eventually created.  To complement the T-34, heavy tanks, self-propelled artillery, and tank destroyers were also designed. The Red Army's armoured forces were used in concentrations during all strategic operations of the Red Army in World War II, initiated under strict secrecy and using the Principle of Surprise.

Germany: In Germany, in-depth research through theoretical approaches, wargaming and exercises developed a confidence within the Panzertruppe itself (and political support by Hitler) in the armoured formation as the key battlefield formation – although this view was before 1940 not shared by the other Arms of Service. A key part of this doctrine was improved communications by having radios in all tanks, although this ideal suffered from technical limits as most tanks had receiver sets only.

At the outbreak of World War II, the German armoured forces benefited from a much more profound and more flexible training than that of the Allies on the tactical and operational level. German tanks operated while directed by radio communication, which allowed tank commanders to take greater advantage of the manoeuvrability of their vehicles.
Even after the conquest of Poland, "Blitzkrieg" was not defined on the strategic level. Guderian and von Manstein devised a strategy that entailed what later would be seen as the essence of Blitzkrieg: concentrated panzer divisions performing swift deep penetrations. This strategy was not initially accepted by German High Command. Nevertheless, the final plans for the invasion of France in 1940 hinged on the element of a Schwerpunkt at Sedan, and was assigned to such forces. The great success of this operation led to Blitzkrieg being integrated with strategic planning for the rest of the war.
German tanks could carry with them enough fuel and supplies to go almost two hundred kilometers, and enough food to last three to nine days. This relative independence from supply lines proved effective, and allowed them to advance on critical targets much faster and without hesitation. Another factor was the ability of commanders to make strategic decisions in the field and without much consultation with their headquarters, the orders of which were often simply ignored. A prime example is Erwin Rommel's lead-from-the-front approach while commanding 7.Panzer-Division which allowed him a flexible response to the battlefield situation, an instance of the Auftragstaktik (reliance on subordinates to make their own decisions).
The effect of German Panzer's speed, mobility, and communication shocked the French, and ultimately were the deciding factors in the battle. It overcame their inferiority in armour and armament relative to the main French materiel such as the Char B1 bis. The superior tactical and operational praxis, combined with an appropriate strategic implementation, enabled the Germans to defeat forces superior in armour (both quantitatively and qualitatively) in the battles of 1940, but just as Blitzkrieg became a deliberate military doctrine, in 1941, it ultimately failed on the eastern front, though initially attaining spectacular successes.
Before the war, Heinz Guderian had in his Achtung–Panzer! propounded a thorough mechanisation of the German forces. By 1942, increased AFV-production allowed a fuller implementation of this ideal. Now extensive armoured combined arms team could be formed, distinct from a purely infantry or cavalry formation. The panzer divisions integrated tanks with mechanised infantry (riding in halftracks to be protected from small-arms fire while being transported) and self-propelled artillery (howitzers fitted on a tank chassis). This allowed the panzer division to become an independent combat force, in principle able to overcome the problems of attaining a breakthrough against entrenched enemy infantry, equipped with large numbers of antitank-guns, with the potential to completely halt tank assaults inflicting devastating losses to armoured units without infantry support. However, much of the AFV production was increasingly diverted away from the Panzertruppe. The Artillery formed its own Sturmgeschütz units and infantry divisions were given their own Panzerjäger companies. Despite lowering their formal organic strength, from the summer of 1943 onwards, the armoured divisions were structurally short of tanks.

United States: Though the U.S. had established the Tank Corps in World War I using French Renault FT light tanks and British Mark V and Mark V* heavy tanks, and some officers like Dwight D. Eisenhower and George S. Patton, Jr. emerged from that war initially as avid proponents of continuing and developing an American armoured force, the rapid reduction of the forces and apathy and even antipathy towards funding and maintaining armed forces in the inter-war years led to relative stagnation of armoured doctrine in the United States. Adna R. Chaffee, Jr., virtually alone, advocated for the future of armoured warfare and the development of appropriate training, equipment and doctrine during the late 1920s through the 1930s.
The United States Army regarded the French Army as the best army in Europe, and consequently the U.S. Army frequently copied French uniforms (the American Civil War) and aeroplanes. Only when France was rapidly overrun in 1940 did the U.S. Army become "shocked" into re-thinking the influences by the perceived actions of German tanks in the 1939 Polish Campaign. Its Armored Combat Arm was not created until 1940 when the Armored Force was born on 10 July 1940, with the Headquarters, Armor Force and the Headquarters, I Armored Corps established at Fort Knox. On July 15, 1940, the 7th Cavalry Brigade (Mechanised) became the 1st Armored Division; the 7th Provisional Tank Brigade, an infantry tank unit at Fort Benning, became the 2nd Armored Division". The Tank Battalion was established at Fort Meade, Md., and a small Armored Force School was also established.
Under this doctrine, U.S. tank crews of both armoured divisions and GHQ tank battalions were taught to fight tanks in tank on tank engagements. Armoured force personnel during and after the war criticised the infantry for using the GHQ tank battalions assigned to infantry divisions strictly as infantry support.

Tank destroyers: The U.S. combined arms team included air support, artillery, engineers, and a tank component supplemented by tank destroyers formed into independent tank destroyer battalions. The latter is most closely identified with the Chief of Army Ground Forces, Lesley J. McNair. Having studied the early German successes McNair came under the belief that U.S. forces would be faced with fast moving enemy forces who would seek to bypass, isolate and reduce U.S. forces in a replay of the Fall of France.  To stem the flood of marauding panzers, fast moving powerfully armed tank destroyer battalions were created to be held back and used in the counter-attack.
It was also calculated that U.S. interests would be better served by large numbers of reliable (battle-worthiness) medium tanks rather than a smaller number of unreliable heavy tanks. It was decided therefore to slow the production of the U.S. heavy tank designs such as the M26 Pershing and concentrate resources on mass-producing the M4 Sherman and tank destroyers such as the M18 Hellcat.
To be able get into position to counter-attack, the tank destroyers had to be fast. To achieve the desired mobility and agility from the engines available the armour protection was sacrificed, a measure of protection coming from being nimble and hopefully from being able to knock out the enemy before they could get a shot in. Although they usually had guns of either 75 mm or 76 mm calibre (the M36 used a 90mm calibre gun), the tank destroyer units were issued with the ancestor of the modern armour-piercing discarding sabot, rounds which made their guns much more powerful than a simple comparison of calibres would suggest.

Japan: The Japanese doctrine was mainly French in concept but with some purely Japanese elements.