Blitzkrieg
That may have been a reason for Hitler to call a halt to the German advance. Those attacks combined with Maxime Weygand's hedgehog tactic would become the major basis for responding to blitzkrieg attacks in the future. Deployment in depth, or permitting enemy or "shoulders" of a penetration, was essential to channelling the enemy attack; artillery, properly employed at the shoulders, could take a heavy toll on attackers. Allied forces in 1940 lacked the experience to develop those strategies successfully, which resulted in the French armistice with heavy losses, but those strategies characterized later Allied operations.
At the Battle of Kursk, the Red Army used a combination of defence in great depth, extensive minefields and tenacious defense of breakthrough shoulders. In that way, they depleted German combat power even as German forces advanced. The reverse can be seen in the Russian summer offensive of 1944, Operation Bagration, which resulted in the destruction of Army Group Center. German attempts to weather the storm and fight out of encirclements failed because of the Soviets' ability to continue to feed armored units into the attack, maintain the mobility and strength of the offensive and arrive in force deep in the rear areas faster than the Germans could regroup.

Logistics: Although effective in quick campaigns against Poland and France, mobile operations could not be sustained by Germany in later years. Strategies based on maneuver have the inherent danger of the attacking force overextending its supply lines and can be defeated by a determined foe who is willing and able to sacrifice territory for time in which to regroup and rearm, as the Soviets did on the Eastern Front, as opposed to, for example, the Dutch, who had no territory to sacrifice. Tank and vehicle production was a constant problem for Germany. Indeed, late in the war, many panzer "divisions" had no more than a few dozen tanks.
As the end of the war approached, Germany also experienced critical shortages in fuel and ammunition stocks as a result of Anglo-American strategic bombing and blockade. Although the production of Luftwaffe fighter aircraft continued, they could not fly because of lack of fuel. What fuel there was went to panzer divisions, and even then, they could not operate normally. Of the Tiger tanks lost against the US Army, nearly half of them were abandoned for lack of fuel.

Military operations: 

Spanish Civil War: German volunteers first used armor in live field-conditions during the Spanish Civil War (1936–1939). Armor commitment consisted of Panzer Battalion 88, a force built around three companies of Panzer I tanks that functioned as a training cadre for Spain's Nationalists. The Luftwaffe deployed squadrons of fighters, dive-bombers and transport aircraft as the Condor Legion. Guderian said that the tank deployment was "on too small a scale to allow accurate assessments to be made". (The true test of his "armored idea" would have to wait for the Second World War.) However, the Luftwaffe also provided volunteers to Spain to test both tactics and aircraft in combat, including the first combat use of the Stuka.
During the war, the Condor Legion undertook the 1937 bombing of Guernica, which had a tremendous psychological effect on the populations of Europe. The results were exaggerated, and the Western Allies concluded that the "city-busting" techniques were now part of the German way in war. The targets of the German aircraft were actually the rail lines and bridges, but lacking the ability to hit them with accuracy (only three or four Ju 87s saw action in Spain), the Luftwaffe chose a method of carpet bombing, resulting in heavy civilian casualties.

Poland, 1939: Although journalists popularized the term Blitzkrieg during the September 1939 invasion of Poland, the historians Matthew Cooper and J. P. Harris have written that German operations during the campaign were consistent with traditional methods. The Wehrmacht strategy was more in line with Vernichtungsgedanke, a focus on envelopment to create pockets in broad-front annihilation. The German generals dispersed Panzer forces among the three German concentrations with little emphasis on independent use. They deployed tanks to create or destroy close pockets of Polish forces and to seize operational-depth terrain in support of the largely-unmotorized infantry, which followed.
The Wehrmacht used available models of tanks, Stuka dive-bombers and concentrated forces in the Polish campaign, but the majority of the fighting involved conventional infantry and artillery warfare, and most Luftwaffe action was independent of the ground campaign. Matthew Cooper wrote:

Throughout the Polish Campaign, the employment of the mechanised units revealed the idea that they were intended solely to ease the advance and to support the activities of the infantry.... Thus, any strategic exploitation of the armoured idea was still-born. The paralysis of command and the breakdown of morale were not made the ultimate aim of the... German ground and air forces, and were only incidental by-products of the traditional maneuvers of rapid encirclement and of the supporting activities of the flying artillery of the Luftwaffe, both of which had as their purpose the physical destruction of the enemy troops. Such was the Vernichtungsgedanke of the Polish campaign.
John Ellis wrote that "there is considerable justice in Matthew Cooper's assertion that the panzer divisions were not given the kind of strategic mission that was to characterize authentic armored blitzkrieg, and were almost always closely subordinated to the various mass infantry armies". Steven Zaloga wrote, "Whilst Western accounts of the September campaign have stressed the shock value of the panzer and Stuka attacks, they have tended to underestimate the punishing effect of German artillery on Polish units. Mobile and available in significant quantity, artillery shattered as many units as any other branch of the Wehrmacht."

Low Countries and France, 1940: The German invasion of France, with subsidiary attacks on Belgium and the Netherlands, consisted of two phases, Operation Yellow (Fall Gelb) and Operation Red (Fall Rot). Yellow opened with a feint conducted against the Netherlands and Belgium by two armored corps and paratroopers. Most of the German armored forces were placed in Panzer Group Kleist, which attacked through the Ardennes, a lightly defended sector that the French planned to reinforce if necessary before the Germans could bring up heavy and siege artillery. There was no time for the French to send such reinforcement, as the Germans did not wait for siege artillery but reached the Meuse and achieved a breakthrough at the Battle of Sedan in three days.
Panzer Group Kleist raced to the English Channel, reached the coast at Abbeville and cut off the BEF, the Belgian Army and some of the best-equipped divisions of the French Army in northern France. Armored and motorized units under Guderian, Rommel and others advanced far beyond the marching and horse-drawn infantry divisions and far in excess of what Hitler and the German high command had expected or wished. When the Allies counter-attacked at Arras by using the heavily armored British Matilda I and Matilda II tanks, a brief panic ensued in the German High Command.
Hitler halted his armored and motorized forces outside the port of Dunkirk, which the Royal Navy had started using to evacuate the Allied forces. Hermann Göring promised that the Luftwaffe would complete the destruction of the encircled armies, but aerial operations failed to prevent the evacuation of the majority of the Allied troops. In Operation Dynamo, some 330,000 French and British troops escaped.
Case Yellow surprised everyone by overcoming the Allies' 4,000 armored vehicles, many of which were better than their German equivalents in armor and gunpower. The French and British frequently used their tanks in the dispersed role of infantry support, rather than by concentrating force at the point of attack, to create overwhelming firepower.

The French armies were much reduced in strength and the confidence of their commanders shaken. With much of their own armor and heavy equipment lost in Northern France, they lacked the means to fight a mobile war. The Germans followed their initial success with Operation Red, a triple-pronged offensive. The XV Panzer Corps attacked towards Brest, XIV Panzer Corps attacked east of Paris, towards Lyon and the XIX Panzer Corps encircled the Maginot Line. The French, hard pressed to organise any sort of counter-attack, were continually ordered to form new defensive lines and found that German forces had already bypassed them and moved on. An armored counter-attack, organized by Colonel Charles de Gaulle, could not be sustained, and he had to retreat.
Prior to the German offensive in May, Winston Churchill had said, "Thank God for the French Army". The same French Army collapsed after barely two months of fighting. That was in shocking contrast to the four years of trench warfare on which French forces had engaged during the First World War. 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.