Military strategy
It was not until the relevant technology (in engineering and communications) matured between the wars that the tank and the airplane could be forged into the co-ordinated force needed to truly restore manoeuvre to warfare.

Inter war: In the years following World War I, two of the technologies that had been introduced during that conflict, the aircraft and the tank, became the subject of strategic study.
The leading theorist of air power was Italian general Giulio Douhet, who believed that future wars would be won or lost in the air. The air force would carry the offensive, and the role of the ground forces would be defensive only. Douhet's doctrine of strategic bombing meant striking at the enemy's heartland—his cities, industry and communications. Air power would thereby reduce his willingness and capacity to fight. At this time the idea of the aircraft carrier and its capabilities also started to change thinking in those countries with large fleets, but nowhere as much as in Japan. The UK and US seem to have seen the carrier as a defensive weapon, and their designs mirrored this; the Japanese Imperial Navy seem to have developed a new offensive strategy based on the power projection these made possible.
British general J. F. C. Fuller, architect of the first great tank battle at Cambrai, and his contemporary, B. H. Liddell Hart, were amongst the most prominent advocates of mechanization and motorization of the army in Britain. In Germany, study groups were set up by Hans von Seeckt, commander of the Reichswehr Truppenamt, for 57 areas of strategy and tactics to learn from World War I and to adapt strategy to avoid the stalemate and then defeat they had suffered. All seem to have seen the strategic shock value of mobility and the new possibilities made possible by motorised forces. Both saw that the armoured fighting vehicle demonstrated firepower, mobility and protection. The Germans seem to have seen more clearly the need to make all branches of the Army as mobile as possible to maximise the results of this strategy. It would negate the static defences of the trench and machine gun and restore the strategic principles of manoeuvre and offense. 
The innovative German Major (later General) Heinz Guderian developed the motorised part of this strategy as the head of one of the Truppenamt groups and may have incorporated Fuller's and Liddell Hart's ideas to amplify the groundbreaking Blitzkrieg effect that was seen used by Germany against Poland in 1939 and later against France in 1940. France, still committed to stationary World War I strategies, was completely surprised and summarily overwhelmed by Germany's mobile combined arms doctrine and Guderian's Panzer Corps.
Technological change had an enormous effect on strategy, but little effect on leadership. The use of telegraph and later radio, along with improved transport, enabled the rapid movement of large numbers of men. One of Germany's key enablers in mobile warfare was the use of radios, where these were put into every tank. However, the number of men that one officer could effectively control had, if anything, declined. The increases in the size of the armies led to an increase in the number of officers. Although the officer ranks in the US Army did swell, in the German army the ratio of officers to total men remained steady.

World War II: 

German: 

Pre-war: Inter-war Germany had as its main strategic goals the re-establishment of Germany as a European great power and the complete annulment of the Versailles treaty of 1919. After Adolf Hitler and the Nazi party  took power in 1933, Germany's political goals also included the accumulation of Lebensraum ("Living space") for the Germanic "race" and the elimination of communism as a political rival to  Nazism.  The destruction of European Jewry, while not strictly a strategic objective, was a political goal of the Nazi regime linked to the vision of a German-dominated Europe, and especially to the Generalplan Ost for a depopulated east which Germany could colonize.
Until the mid-1930s, Germany's ability to realize these goals was limited by its weakened military and economic position. Hitler's strategy involved building up German military and economic strength through re-armament, while seeking to avoid an early war by diplomatic engagement with France, Britain and (later) the Soviet Union (Stalin-Hitler Pact of August 1939). One by one, Hitler successfully repudiated the terms the Versailles treaty, using skilful diplomacy to avoid triggering war. After starting open re-armament in 1935, he carried out the re-occupation of the Rhineland in 1936, and then the diplomatic annexation of Austria (Anschluss) and of Czechoslovakia in 1938 and 1939 (Munich Agreement, September 1938). This risky political strategy proved initially successful, consolidating internal support for the Nazi regime and greatly strengthening Germany's strategic position.
But the March 1939 annexation of rump Czechoslovakia, in violation of the Munich Agreement signed only months before, forced a change in Franco-British policy from an emphasis on avoiding war (Appeasement) to an emphasis on war preparation, of which an important feature was the declaration of  Franco-British guarantees of Polish independence. When Germany invaded Poland in September 1939, Britain and France declared war (3 September 1939).

War strategy: Hitler's strategy for war was laid out in Mein Kampf (1925/1926). Whether Hitler intended global or merely European conquest, or whether he even had a plan for war in advance is debated; see Nazi foreign policy (historiographic debate). In Mein Kampf, Hitler had imagined a short war against France, and then the conquest of the USSR. He had wrongly assumed that Britain would be a German ally in the west against France, and so he did not foresee an enduring war in the west.
Once the Second World War had begun with France and Britain as allies, German strategy aimed to win a short war in France and to force Britain to the negotiating table. After the  conquest of France in May–June 1940, Churchill's refusal to surrender or to negotiate on terms favorable for Germany put the German gamble in jeopardy. Germany could not match Britain on the open sea and had not prepared its army for operations across the Channel. Instead, the Wehrmacht hoped to strangle Britain's economy through success in the Battle of the Atlantic (1939–1945) and the Battle of Britain (1940).
In June 1941 Germany invaded the USSR (Operation Barbarossa) to carry out the second part of Hitler's strategy. The campaign plan envisaged  defeating the USSR in a single summer / fall campaign, but Barbarossa failed to achieve any of its major objectives. In December 1941 Japan attacked the USA and Germany declared war on the USA shortly afterwards. Through the summer and fall of 1942, German strategy to win the war remained based on defeating the USSR.

British: Since the Entente Cordiale which had won the First World War, Britain's strategy for continental war was based on alliance with France and later unsuccessful efforts to engage Fascist Italy and the USSR in an effort to contain Germany. Confronted with the rise of Hitler's power on the continent in 1933, and weakened economically by the Great Depression, Great Britain sought initially to avoid or delay war through diplomacy (Appeasement), while at the same time re-arming (Neville Chamberlain's European Policy). Emphasis for re-armament was given to air forces with the view that these would be most useful in any future war with Germany.
By 1939, Allied efforts to avert war had failed, and Germany had signed alliances with both Italy (Pact of Steel) and the USSR (Molotov–Ribbentrop Pact). In August 1939, in a final effort to contain Germany, Britain and France guaranteed Polish independence (Anglo-Polish military alliance).
Upon the outbreak of war in September 1939, British rearmament was not yet complete, although the Royal Air Force had been greatly expanded and programmes for new aircraft and equipment such as radar defences were just coming to fruition. Britain remained incapable of offensive operations except for strategic bombing, and this was relatively ineffective in the early war.
After the fall of France in mid 1940 and Italian entry into the war on the Axis side, Britain and its commonwealth allies found themselves alone against most of Europe. British strategy was one of survival, defending the British isles directly in the Battle of Britain and indirectly by defeating Germany in the Battle of the Atlantic and the combined Axis powers in the North African Campaign. Through this period, and until the German invasion of the USSR in June 1941, there was no possibility of Britain winning the war alone, and so British Grand Strategy aimed to bring the USA into the war on the allied side. Prime Minister Churchill devoted much of his diplomatic efforts to this goal. In August 1941, at the Atlantic Conference he met US President Roosevelt in the first of many wartime meetings wherein allied war strategy was jointly decided.
In December 1941, following the Japanese attack on Pearl Harbor, the United States entered the war. Britain was now also at war with imperial Japan, whose forces inflicted rapid defeats on British forces in Asia, capturing Hong Kong, Malaya, Singapore and Burma. Nevertheless, Churchill expressed the view that with the entry of the USA into the war, ultimate victory was assured for the Allies. "All the rest was merely the proper application of overwhelming force".