Armoured warfare
Despite the increase in tank numbers, in all countries financial constraints prohibited a full mechanisation of the entire armed ground forces. Necessarily, most of the divisions still consisted of infantry that was not even motorised. As a result, tanks tended to be allotted to special armoured units, where the limited and expensive expert maintenance and training capacity could be concentrated. Only the Soviet Union had enough tanks to equip an organic tank battalion in each infantry division. Nevertheless, France was the first to create large armoured units: in 1934 two Mechanised Corps were formed of 430 tanks each. In July 1935, in France the 4th Cavalry Division was transformed into the 1e Division Légère Mécanique, the first French armoured division of the Cavalry. In Germany, after the Nazi Regime started open rearmament in March 1935, on 15 October 1935 three Panzerdivisionen were formed. Though some tank brigades were part of the Cavalry or Infantry arm, most German tanks were concentrated into a special branch, from 1936 called the Panzerwaffe. The precise interpretation of this phenomenon has proven controversial among military historians. Traditionally, it has been seen as part of a "Blitzkrieg strategy" of swift world conquest by means of armoured forces. Later it has been argued, among others by Karl-Heinz Frieser, that the German army in the 1930s did not even possess an explicit Blitzkrieg tactical doctrine, let alone strategy. This would have been reflected by the relatively unimpressive rate of tank production and development. During the 1930s the United Kingdom gave priority to the Royal Air Force and Royal Navy. The British Army began the conversion of its cavalry from horse to tanks and all but a few regiments were fully converted by 1939. The British 1st Armoured Division was formed, as the "Mobile Division", in November 1937.
Before the Second World War actual use of armoured fighting vehicles was limited. Both sides used Italian, German and Soviet tanks during the Spanish Civil War but these proved to be vulnerable to antitank guns due to their thin armour. Traditionalist elements within the Red Army used this to diminish the influence of proponents of mechanisation. Tukhachevsky himself was executed in 1937. Nevertheless, during the Soviet-Japanese Border Wars of 1938 and 1939, the Soviet forces tested modern armoured warfare tactics. General Georgy Zhukov in the summer of 1939 combined mass tank manoeuvres with artillery and air attacks, to defeat the Japanese Imperial Army at the Battles of Khalkhin Gol at Nomonhan in Mongolia. Partly as a result of the experiences in Spain, the Soviet Union began the development of a new generation of medium and heavy tanks, sporting much stronger armour and armament.

World War II: 

Poland: In their Invasion of Poland during September 1939, German forces applied a narrow cooperation between large armoured units – of the Panzerwaffe and the Cavalry – and "active" infantry divisions to break the Polish defensive lines and pursue the defeated enemy forces. The more limited and dispersed Polish armoured units were quickly destroyed. The Red Army, invading the east of Poland, also deployed armoured divisions. At the time, the swift collapse of the Polish army was seen as the result of an armoured Blitzkrieg. However, later it has been argued that the campaign was largely an instance of the classical nineteenth century German concept of the "Annihilation Battle", in which the role of deep strategic armoured penetrations was limited.

France: In the wake of the Polish campaign, during the Phoney War French, British and German tank production sharply increased, with both western allies out-producing Germany. However, the Anglo-French coalition proved unable to match the Germans in the number of armoured divisions, as it was impossible to quickly raise such large units. Though the French possessed a superior number of tanks, often better armoured and armed, half of these were allotted at army-level to independent Bataillons de Chars de Combat ("battle tank battalions") for infantry support. In early 1940, the German command had concluded that it could not win a war of attrition and embarked on a high-risk strategy. They approved the Manstein Plan, envisaging an advance through the Ardennes by the main mass of German infantry divisions, spearheaded by seven armoured divisions, while the main mobile French reserve consisting of three Cavalry armoured divisions (Divisions Légères Mécaniques or Mechanised Light Divisions) – the only armoured units organised on the lines of the German armoured divisions – would be lured into the Low Countries by a feint attack with a lesser force, including three armoured divisions. In May 1940, during the Battle of France, the German feint resulted in a number of undecided armour engagements, among them the Battle of Hannut, the largest tank battle fought until that date. At the same time, German motorised infantry west of the Ardennes forced the crossings over the river Meuse, assisted by massive carpet bombing of the crossing points. In the original plan, the armoured divisions were again supposed to closely cooperate with the infantry divisions. In reality, armour commanders like Erwin Rommel and Heinz Guderian immediately broke out of the bridgeheads, initiating a drive towards the English Channel, which was reached within a week. The French reserve of four Infantry armoured divisions, the Divisions cuirassées, lacked sufficient strategic mobility to prevent this. The strategic envelopment surrounded the Belgian army, the British Expeditionary Force and the best French troops. It led to the Evacuation of Dunkirk and the ultimate fall of France in operation Fall Rot.
The spectacular and unexpected success not only caused a sudden change in the global geostrategic situation, gaining Germany a position of hegemony on the European continent, but also seemed to vindicate the theories of Fuller and Liddell-Hart. Confronted with the undeniable potential of armoured manoeuvre warfare, from the summer of 1940 onwards the armed forces of all surviving major powers adapted their tactical doctrine, unit organisation, strategic planning and tank production plans. According to Frieser, this was even true for Germany itself, that only now officially adopted Blitzkrieg tactics.

North African theatre: In the deserts of North Africa, the British developed the alternative approach of combining the armoured, infantry and artillery together to form a 'balanced, combined arms team'. The 10th Italian Army of Maresciallo (Marshal) Rodolfo Graziani, being ill-armed and inadequately led, soon gave way to this approach by the Commonwealth troops of the British Western Desert Force.
The arrival of the German Afrika Korps under command of General der Panzertruppe Erwin Rommel highlighted the weaknesses of the British approach: the small number of infantry and artillery in each armoured division was sufficient when attacking the immobile and uncoordinated Italian troops, but against the highly mobile, well-coordinated German units, the undermanned Commonwealth formations were proving inadequate. 
Between 1941 and 1942, the Allies struggled in armoured battles in the North African desert due to improper tactics; in particular, running armoured formations into opposing anti-tank positions; however, they achieved some notable successes at Crusader, 1st Alamein and under Montgomery finally achieved decisive victories, in particular at the Second Battle of El Alamein.
In 2022, Kendrick Kuo, assistant professor at the U.S. Naval War College, wrote that due to factors emanating from the interwar period, the British army in North Africa initially operated their armoured units with little infantry or artillery support. Meanwhile, the Germans had integrated their armour with mechanised infantry and artillery. Only after undoing their misplaced emphasis on armour were the British able to restore their combat effectiveness.

Soviet Union: 

Pre-war: Much of the Red Army development in tank use was based on the theoretical work carried out by such officers as Tukhachevsky and Triandafillov in the mid to late 1930s. This was as part of the two-directioned concepts, one being infantry-centred "broad front" and the other being a "shock army".
While the infantry based part of the doctrine demanded "powerful tanks" (heavy tanks armed with infantry guns and machineguns) and "tankettes" (light, often amphibious tanks with machineguns), the shock army demanded "manoeuvre tanks" (fast tanks with medium guns) used in conjunction with motorised forces and "mechanised cavalry" that would operate in depth as "strategic cavalry" combined with nascent airborne troops.
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.