Wehrmacht
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.) forces and the Axis forces
The Italian Theatre was a continuation of the Axis defeat in North Africa, and was a campaign for defence of Italy

Casualties: More than 6,000,000 soldiers were wounded during the conflict, while more than 11,000,000 became prisoners. In all, approximately 5,318,000 soldiers from Germany and other nationalities fighting for the German armed forces—including the Waffen-SS, Volkssturm and foreign collaborationist units—are estimated to have been killed in action, died of wounds, died in custody or gone missing in World War II. Included in this number are 215,000 Soviet citizens conscripted by Germany.
According to Frank Biess,

German casualties took a sudden jump with the defeat of the Sixth Army at Stalingrad in January 1943, when 180,310 soldiers were killed in one month. Among the 5.3 million Wehrmacht casualties during the Second World War, more than 80 per cent died during the last two years of the war. Approximately three-quarters of these losses occurred on the Eastern front (2.7 million) and during the final stages of the war between January and May 1945 (1.2 million).
Jeffrey Herf wrote that:

Whereas German deaths between 1941 and 1943 on the western front had not exceeded three per cent of the total from all fronts, in 1944 the figure jumped to about 14 per cent. Yet even in the months following D-day, about 68.5 per cent of all German battlefield deaths occurred on the eastern front, as a Soviet blitzkrieg in response devastated the retreating Wehrmacht.
In addition to the losses, at the hands of the elements and enemy fighting, at least 20,000 soldiers were executed as sentences by the military court. In comparison, the Red Army executed 135,000, France 102, the US 146 and the UK 40.

War crimes: Nazi propaganda had told Wehrmacht soldiers to wipe out what were variously called Jewish Bolshevik subhumans, the Mongol hordes, the Asiatic flood and the red beast. While the principal perpetrators of the civil suppression behind the front lines amongst German armed forces were the Nazi German "political" armies (the SS-Totenkopfverbände, the Waffen-SS, and the Einsatzgruppen, which were responsible for mass-murders, primarily by implementation of the so-called Final Solution of the Jewish Question in occupied territories), the traditional armed forces represented by the Wehrmacht committed and ordered war crimes of their own (e.g. the Commissar Order), particularly during the invasion of Poland in 1939 and later in the war against the Soviet Union.

Cooperation with the SS: Prior to the outbreak of war, Hitler informed senior Wehrmacht officers that actions "which would not be in the taste of German generals", would take place in occupied areas and ordered them that they "should not interfere in such matters but restrict themselves to their military duties". Some Wehrmacht officers initially showed a strong dislike for the SS and objected to the army committing war crimes with the SS, though these objections were not against the idea of the atrocities themselves. Later during the war, relations between the SS and Wehrmacht improved significantly. The common soldier had no qualms with the SS, and often assisted them in rounding up civilians for executions.
The Army's Chief of Staff General Franz Halder in a directive declared that in the event of guerrilla attacks, German troops were to impose "collective measures of force" by massacring entire villages. Cooperation between the SS Einsatzgruppen and the Wehrmacht involved supplying the death squads with weapons, ammunition, equipment, transport, and even housing. Partisan fighters, Jews, and Communists became synonymous enemies of the Nazi regime and were hunted down and exterminated by the Einsatzgruppen and Wehrmacht alike, something revealed in numerous field journal entries from German soldiers. With the implementation of the Hunger Plan, hundreds of thousands, perhaps millions, of Soviet civilians were deliberately starved to death, as the Germans seized food for their armies and fodder for their draft horses. According to Thomas Kühne: "an estimated 300,000–500,000 people were killed during the Wehrmacht's Nazi security warfare in the Soviet Union."
While secretly listening to conversations of captured German generals, British officials became aware that the German Army had taken part in the atrocities and mass-murder of Jews and were guilty of war crimes. American officials learned of the Wehrmacht's atrocities in much the same way. Taped conversations of soldiers detained as POWs revealed how some of them voluntarily participated in mass executions.

Crimes against civilians: During the war, the Wehrmacht committed numerous war crimes against the civilian population in occupied countries. This includes massacres of civilians and running forced brothels in occupied areas.
Massacres would in many cases come as reprisals for acts of resistance. With these reprisals, the Wehrmacht's response would vary in severity and method, depending on the scale of resistance and whether it was in East or West Europe. Often, the number of hostages to be shot was calculated based on a ratio of 100 hostages executed for every German soldier killed and 50 hostages executed for every German soldier wounded. Other times civilians would be rounded up and shot with machine guns.
To combat German officials' fear of venereal disease and masturbation, the Wehrmacht established numerous brothels throughout Nazi Germany and its occupied territories. Women would often be kidnapped off the streets and forced to work in the brothels, with an estimated minimum of 34,140 women being forced to serve as prostitutes.

Crimes against POWs: While the Wehrmacht's prisoner-of-war camps for inmates from the west generally satisfied the humanitarian requirement prescribed by international law, prisoners from Poland and the USSR were incarcerated under significantly worse conditions. Between the launching of Operation Barbarossa in the summer of 1941 and the following spring, 2.8 million of the 3.2 million Soviet prisoners taken died while in German hands.

Criminal and genocidal organization: Among German historians, the view that the Wehrmacht had participated in wartime atrocities, particularly on the Eastern Front, grew in the late 1970s and the 1980s. In the 1990s, public conception in Germany was influenced by controversial reactions and debates about the exhibition of war crime issues.
Holocaust historian Omer Bartov, a leading expert on the Wehrmacht, wrote in 2003 that the Wehrmacht was a willing instrument of genocide and that it is untrue that the Wehrmacht was an apolitical, professional fighting force that had only a few "bad apples". Bartov argues that far from being the "untarnished shield", as successive German apologists stated after the war, the Wehrmacht was a criminal organization. Likewise, the historian Richard J. Evans, a leading expert on modern German history, wrote that the Wehrmacht was a genocidal organization. The historian Ben H. Shepherd writes that "There is now clear agreement amongst historians that the German Wehrmacht ... identified strongly with National Socialism and embroiled itself in the criminality of the Third Reich." British historian Ian Kershaw concludes that the Wehrmacht's duty was to ensure that the people who met Hitler's requirements of being part of the Aryan Herrenvolk ("Aryan master race") had living space. He wrote that:

The Nazi revolution was broader than just the Holocaust. Its second goal was to eliminate Slavs from central and eastern Europe and to create a Lebensraum for Aryans. ... As Bartov (The Eastern Front; Hitler's Army) shows, it barbarised the German armies on the eastern front. Most of their three million men, from generals to ordinary soldiers, helped exterminate captured Slav soldiers and civilians. This was sometimes cold and deliberate murder of individuals (as with Jews), sometimes generalised brutality and neglect. ... German soldiers' letters and memoirs reveal their terrible reasoning: Slavs were 'the Asiatic-Bolshevik' horde, an inferior but threatening race.
Several high-ranking Wehrmacht officers, including Hermann Hoth, Georg von Küchler, Georg-Hans Reinhardt, Karl von Roques, Walter Warlimont and others, were convicted of war crimes and crimes against humanity at the High Command Trial given sentences ranging from time served to life.

Resistance to the Nazi regime: Originally, there was little resistance within the Wehrmacht, as Hitler actively went against the Treaty of Versailles and attempted to recover the army's honor. The first major resistance began in 1938 with the Oster conspiracy, where several members of the military wanted to remove Hitler from power, as they feared a war with Czechoslovakia would ruin Germany. However, following the success of the early campaigns in Poland, Scandinavia and France, belief in Hitler was restored. With the defeat in Stalingrad, trust in Hitler's leadership began to wane. This caused an increase in resistance within the military. The resistance culminated in the 20 July plot (1944), when a group of officers led by Claus von Stauffenberg attempted to assassinate Hitler.