Blitzkrieg
French Prime Minister Paul Reynaud, analyzed the collapse in a speech on 21 May 1940:

The truth is that our classic conception of the conduct of war has come up against a new conception. At the basis of this... there is not only the massive use of heavy armoured divisions or cooperation between them and airplanes, but the creation of disorder in the enemy's rear by means of parachute raids.
The Germans had not used paratroopry attacks in France and made only one large drop in the Netherlands to capture three bridges; some small glider-landings were conducted in Belgium to take bottlenecks on routes of advance before the arrival of the main force (the most renowned being the landing on Fort Eben-Emael in Belgium).

Eastern Front, 1941–44: Use of armored forces was crucial for both sides on the Eastern Front. Operation Barbarossa, the German invasion of the Soviet Union in June 1941, involved a number of breakthroughs and encirclements by motorized forces. Its goal, according to Führer Directive 21 (18 December 1940), was "to destroy the Russian forces deployed in the West and to prevent their escape into the wide-open spaces of Russia". The Red Army was to be destroyed west of the Dvina and Dnieper rivers, which were about 500 kilometres (310 mi) east of the Soviet border, to be followed by a mopping-up operation. The surprise attack resulted in the near annihilation of the Voyenno-Vozdushnye Sily (VVS, Soviet Air Force) by simultaneous attacks on airfields, allowing the Luftwaffe to achieve total air supremacy over all the battlefields within the first week. On the ground, four German panzer groups outflanked and encircled disorganized Red Army units, and the marching infantry completed the encirclements and defeated the trapped forces. In late July, after 2nd Panzer Group (commanded by Guderian) captured the watersheds of the Dvina and Dnieper rivers near Smolensk, the panzers had to defend the encirclement, because the marching infantry divisions remained hundreds of kilometers to the west.
The Germans conquered large areas of the Soviet Union, but their failure to destroy the Red Army before the winter of 1941-1942 was a strategic failure and made German tactical superiority and territorial gains irrelevant. The Red Army had survived enormous losses and regrouped with new formations far to the rear of the front line. During the Battle of Moscow (October 1941 to January 1942), the Red Army defeated the German Army Group Center and for the first time in the war seized the strategic initiative.
In the summer of 1942, Germany launched another offensive and this time focusing on Stalingrad and the Caucasus in the southern Soviet Union. The Soviets again lost tremendous amounts of territory, only to counter-attack once more during winter. The German gains were ultimately limited because Hitler diverted forces from the attack on Stalingrad and drove towards the Caucasus oilfields simultaneously. The Wehrmacht became overstretched. Although it won operationally, it could not inflict a decisive defeat as the durability of the Soviet Union's manpower, resources, industrial base and aid from the Western Allies began to take effect.
In July 1943, the Wehrmacht conducted Operation Zitadelle (Citadel) against a salient at Kursk, which Soviet troop heavily defended. Soviet defensive tactics had by now hugely improved, particularly in the use of artillery and air support. By April 1943, the Stavka had learned of German intentions through intelligence supplied by front-line reconnaissance and Ultra intercepts. In the following months, the Red Army constructed deep defensive belts along the paths of the planned German attack. The Soviets made a concerted effort to disguise their knowledge of German plans and the extent of their own defensive preparations, and the German commanders still hoped to achieve operational surprise when the attack commenced.
The Germans did not achieve surprise and could not outflank or break through into enemy rear areas during the operation. Several historians assert that Operation Citadel was planned and intended to be a blitzkrieg operation. Many of the German participants who wrote about the operation after the war, including Erich von Manstein, make no mention of blitzkrieg in their accounts. In 2000, Niklas Zetterling and Anders Frankson characterised only the southern pincer of the German offensive as a "classical blitzkrieg attack". Pier Battistelli wrote that the operational planning marked a change in German offensive thinking away from blitzkrieg and that more priority was given to brute force and fire power than to speed and maneuver.
In 1995, David Glantz stated that blitzkrieg was at Kursk for the first time defeated in summer, and the opposing Soviet forces mounted a successful counter-offensive. The Battle of Kursk ended with two Soviet counter-offensives and the revival of deep operations. In the summer of 1944, the Red Army destroyed Army Group Centre in Operation Bagration by using combined-arms tactics for armor, infantry and air power in a coordinated strategic assault, known as deep operations, which led to an advance of 600 kilometres (370 mi) in six weeks.

Western Front, 1944–1945: Allied armies began using combined-arms formations and deep-penetration strategies that Germany had used in the opening years of the war. Many Allied operations in the Western Desert and on the Eastern Front, relied on firepower to establish breakthroughs by fast-moving armored units. The artillery-based tactics were also decisive in Western Front operations after 1944's Operation Overlord, and the British Commonwealth and American armies developed flexible and powerful systems for using artillery support. What the Soviets lacked in flexibility, they made up for in number of rocket launchers, guns and mortars. The Germans never achieved the kind of fire concentrations that their enemies were achieving 1944.
After the Allied landings in Normandy (June 1944), the Germans began a counter-offensive to overwhelm the landing force with armored attacks, but they failed because of a lack of co-ordination and to Allied superiority in anti-tank defense and in the air. The most notable attempt to use deep-penetration operations in Normandy was Operation Luttich at Mortain, which only hastened the Falaise Pocket and the destruction of German forces in Normandy. The Mortain counter-attack was defeated by the American 12th Army Group with little effect on its own offensive operations.
The last German offensive on the Western front, the Battle of the Bulge (Operation Wacht am Rhein), was an offensive launched towards the port of Antwerp in December 1944. Launched in poor weather against a thinly-held Allied sector, it achieved surprise and initial success as Allied air-power was grounded due to cloud cover. Determined defense by American troops in places throughout the Ardennes, the lack of good roads and German supply shortages caused delays. Allied forces deployed to the flanks of the German penetration, and as soon as the skies cleared, Allied aircraft returned to the battlefield. Allied counter-attacks soon forced back the Germans, who abandoned much equipment for lack of fuel.

Post-war controversy: Blitzkrieg had been called a Revolution in Military Affairs (RMA), but many writers and historians have concluded that the Germans did not invent a new form of warfare but applied new technologies to traditional ideas of Bewegungskrieg (maneuver warfare) to achieve decisive victory.

Strategy: In 1965, Captain Robert O'Neill, Professor of the History of War at the University of Oxford produced an example of the popular view. In Doctrine and Training in the German Army 1919–1939, O'Neill wrote:

What makes this story worth telling is the development of one idea: the blitzkrieg. The German Army had a greater grasp of the effects of technology on the battlefield, and went on to develop a new form of warfare by which its rivals when it came to the test were hopelessly outclassed.
Other historians wrote that blitzkrieg was an operational doctrine of the German armed forces and a strategic concept on which the leadership of Nazi Germany based its strategic and economic planning. Military planners and bureaucrats in the war economy appear rarely, if ever, to have employed the term blitzkrieg in official documents. That the German army had a "blitzkrieg doctrine" was rejected in the late 1970s by Matthew Cooper. The concept of a blitzkrieg Luftwaffe was challenged by Richard Overy in the late 1970s and by Williamson Murray in the mid-1980s. That Nazi Germany went to war on the basis of "blitzkrieg economics" was criticized by Richard Overy in the 1980s, and George Raudzens described the contradictory senses in which historians have used the word. The notion of a German blitzkrieg concept or doctrine survives in popular history and many historians still support the thesis.
Frieser wrote that after the failure of the Schlieffen Plan in 1914, the German army concluded that decisive battles were no longer possible in the changed conditions of the twentieth century. Frieser wrote that the Oberkommando der Wehrmacht (OKW), which was created in 1938 had intended to avoid the decisive battle concepts of its predecessors and planned for a long war of exhaustion (Ermattungskrieg). It was only after the improvised plan for the Battle of France in 1940 was unexpectedly successful that the German General Staff came to believe that Vernichtungskrieg was still feasible.