Wehrmacht
These tanks were used to break through enemy lines, isolating regiments from the main force so that the infantry behind the tanks could quickly kill or capture the enemy troops.

Air Force: Originally outlawed by the Treaty of Versailles, the Luftwaffe was officially established in 1935, under the leadership of Hermann Göring. First gaining experience in the Spanish Civil War, it was a key element in the early Blitzkrieg campaigns (Poland, France 1940, USSR 1941). The Luftwaffe concentrated production on fighters and (small) tactical bombers, like the Messerschmitt Bf 109 fighter and the Junkers Ju 87 Stuka dive bomber. The planes cooperated closely with the ground forces. Overwhelming numbers of fighters assured air-supremacy, and the bombers would attack command- and supply-lines, depots, and other support targets close to the front. The Luftwaffe would also be used to transport paratroopers, as first used during Operation Weserübung. Due to the Army's sway with Hitler, the Luftwaffe was often subordinated to the Army, resulting in it being used as a tactical support role and losing its strategic capabilities.
The Western Allies' strategic bombing campaign against German industrial targets (particularly the round-the-clock Combined Bomber Offensive) and Germany's Defence of the Reich deliberately forced the Luftwaffe into a war of attrition. With German fighter force destroyed, the Western Allies had air supremacy over the battlefield, denying support to German forces on the ground and using its own fighter-bombers to attack and disrupt. Following the losses in Operation Bodenplatte in 1945, the Luftwaffe was no longer an effective force.

Navy: The Treaty of Versailles disallowed submarines, while limiting the size of the Reichsmarine to six battleships, six cruisers, and twelve destroyers. Following the creation of the Wehrmacht, the navy was renamed the Kriegsmarine.
With the signing of the Anglo-German Naval Agreement, Germany was allowed to increase its navy's size to be 35:100 tonnage of the Royal Navy, and allowed for the construction of U-boats. This was partly done to appease Germany, and because Britain believed the Kriegsmarine would not be able to reach the 35% limit until 1942. The navy was also prioritized last in the German rearmament scheme, making it the smallest of the branches.
In the Battle of the Atlantic, the initially successful German U-boat fleet arm was eventually defeated due to Allied technological innovations like sonar, radar, and the breaking of the Enigma code.
Large surface vessels were few in number due to construction limitations by international treaties prior to 1935. The "pocket battleships" Admiral Graf Spee and Admiral Scheer were important as commerce raiders only in the opening year of the war. No aircraft carrier was operational, as German leadership lost interest in the Graf Zeppelin which had been launched in 1938.
Following the loss of the German battleship Bismarck in 1941, with Allied air-superiority threatening the remaining battle-cruisers in French Atlantic harbors, the ships were ordered to make the Channel Dash back to German ports. Operating from fjords along the coast of Norway, which had been occupied since 1940, convoys from North America to the Soviet port of Murmansk could be intercepted though the Tirpitz spent most of her career as fleet in being. After the appointment of Karl Dönitz as Grand Admiral of the Kriegsmarine (in the aftermath of the Battle of the Barents Sea), Germany stopped constructing battleships and cruisers in favor of U-boats. Though by 1941, the navy had already lost a number of its large surface ships, which could not be replenished during the war.
The Kriegsmarine's most significant contribution to the German war effort was the deployment of its nearly 1,000 U-boats to strike at Allied convoys. The German naval strategy was to attack the convoys in an attempt to prevent the United States from interfering in Europe and to starve out the British. Karl Doenitz, the U-Boat Chief, began unrestricted submarine warfare which cost the Allies 22,898 men and 1,315 ships. The U-boat war remained costly for the Allies until early spring of 1943 when the Allies began to use countermeasures against U-Boats such as the use of Hunter-Killer groups, airborne radar, torpedoes and mines like the FIDO. The submarine war cost the Kriegsmarine 757 U-boats, with more than 30,000 U-boat crewmen killed.

Coexistence with the Waffen-SS: In the beginning, there was friction between the SS and the army, as the army feared the SS would attempt to become a legitimate part of the armed forces of Nazi Germany, partly due to the fighting between the limited armaments, and the perceived fanaticism towards Nazism. However, on 17 August 1938, Hitler codified the role of the SS and the army in order to end the feud between the two. The arming of the SS was to be "procured from the Wehrmacht upon payment", however "in peacetime, no organizational connection with the Wehrmacht exists." The army was however allowed to check the budget of the SS and inspect the combat readiness of the SS troops. In the event of mobilization, the Waffen-SS field units could be placed under the operational control of the OKW or the OKH. All decisions regarding this would be at Hitler's personal discretion.
Though there existed conflict between the SS and Wehrmacht, many SS officers were former army officers, which ensured continuity and understanding between the two. Throughout the war, army and SS soldiers worked together in various combat situations, creating bonds between the two groups. Guderian noted that every day the war continued the Army and the SS became closer together. Towards the end of the war, army units would even be placed under the command of the SS, in Italy and the Netherlands. The relationship between the Wehrmacht and the SS improved; however, the Waffen-SS was never considered "the fourth branch of the Wehrmacht."

Theatres and campaigns: The Wehrmacht directed combat operations during World War II (from 1 September 1939 – 8 May 1945) as the German Reich's armed forces umbrella command-organization. After 1941 the OKH became the de facto Eastern Theatre higher-echelon command-organization for the Wehrmacht, excluding Waffen-SS except for operational and tactical combat purposes. The OKW conducted operations in the Western Theatre. The operations by the Kriegsmarine in the North and Mid-Atlantic can also be considered as separate theatres, considering the size of the area of operations and their remoteness from other theatres.
The Wehrmacht fought on other fronts, sometimes three simultaneously; redeploying troops from the intensifying theatre in the East to the West after the Normandy landings caused tensions between the General Staffs of both the OKW and the OKH – as Germany lacked sufficient materiel and manpower for a two-front war of such magnitude.

Eastern theatre: Major campaigns and battles in Eastern and Central Europe included:

Czechoslovakian campaign (1938–1945)
Invasion of Poland (Fall Weiss)
Operation Barbarossa (1941), conducted by Army Group North, Army Group Centre, and Army Group South
Battle of Moscow (1941)
Battles of Rzhev (1942–1943)
Battle of Stalingrad (1942–1943)
Battle of the Caucasus (1942–1943)
Battle of Kursk (Operation Citadel) (1943)
Battle of Kiev (1943)
Operation Bagration (1944)
Nazi security warfare – largely carried out by security divisions of the Wehrmacht, Order Police and Waffen-SS units in the occupied territories behind Axis frontlines.

Western theatre: Phoney War (Sitzkrieg, September 1939 to May 1940) between the invasion of Poland and the Battle of France
Operation Weserübung
German invasion of Denmark – 9 April 1940
The Norwegian Campaign – 9 April to 10 June 1940
Fall Gelb
Battle of Belgium 10 to 28 May 1940
German invasion of Luxembourg 10 May 1940
Battle of the Netherlands – 10 to 17 May 1940
Battle of France – 10 May to 25 June 1940
Battle of Britain (1940)
Battle of the Atlantic (1939–1945)
Battle of Normandy (1944)
Allied invasion of southern France (1944)
Ardennes Offensive (1944–1945)
Defense of the Reich air-campaign, 1939 to 1945

Mediterranean theatre: For a time, the Axis Mediterranean Theatre and the North African Campaign were conducted as a joint campaign with the Italian Army, and may be considered a separate theatre.

Invasion of the Balkans and Greece (Operation Marita) (1940–1941)
Battle of Crete (1941)
The North African Campaign in Libya, Tunisia and Egypt between the UK and Commonwealth (and later, U.S.)