(Full name: Einsatzgruppen der Sicherheitsdienstes [SD] und der Sicherheitspolizei [SIPO]).
German term, meaning "action-groups," that originally referred to Nazi police intelligence units that worked with the German army following the invasion of Austria, Czechoslovakia, and Poland. Later, the term referred to mobile SS killing units that traveled with the German forces that invaded the Soviet Union in 1941.
When the Germans invaded Austria in March 1938 and Czechoslovakia in March 1939, the Einsatzgruppen’s role was to follow the advancing military and serve as portable offices of the Nazis' Security Service and Security Police until permanent offices could be set up. The Einsatzgruppen were in charge of security in these regions, which involved locating and imprisoning opponents of the Nazis.
In preparation for the Nazi invasion of Poland in September 1939, the Einsatzgruppen were commanded to combat elements deemed hostile to the Reich; this was interpreted as an order to murder thousands of Jews and members of the Polish upper class. Soon after, on September 21, 1939, the Einsatzgruppen received instructions concerning Jews in the newly conquered regions: they were to arrest and transfer them to ghettos near railway lines, in order to facilitate future population movement. They were also instructed to set up Judenraete (Jewish Councils). These Einsatzgruppen were disbanded in November 1939; their members joined the permanent Security Services and Security Police offices in occupied Poland.
As Germany prepared to invade the Soviet Union in June 1941, Hitler made it clear to the army that the upcoming war was based on a fundamental conflict between two completely opposing ideologies. It was imperative to destroy those elements that perpetuated the conflicting ideology. Thus, special units called Einsatzgruppen were formed to accompany the advancing military forces. Their job was to search for opponents of the Reich, including Communists and all Jews—and execute them.
When Operation "Barbarossa" began, the Einsatzgruppen followed the German army Wehrmacht into the Soviet Union. Four units had been established, Einsatzgruppen A, B, C, and D. Each was assigned to liquidate the Jews in its region, and each was divided into sub-units called Sonderkommandos or Einsatzkommandos. Einsatzgruppe A, the largest group with about 1,000 men, was attached to Army Group North. They operated in the Baltic States (Lithuania, Latvia, and Estonia) and the area between their eastern borders and Leningrad. Einsatzgruppe B, 655 men attached to Army Group Center, worked in Belorussia and the Smolensk district, east of Moscow. Einsatzgruppe C, a group of 700 attached to Army Group South, covered the northern and central Ukraine. Einsatzgruppe D, with 600 men attached to the Eleventh Army, operated in the southern Ukraine, the Crimea, and Ciscaucasia. These groups did not carry out the destruction of Soviet Jewry alone—they were regularly assisted by other German soldiers, German police units and local collaborators in various locations. By the spring of 1943, the Einsatzgruppen had exterminated 1.25 million Jews and hundreds of thousands of Soviets, including prisoners of war.
The Einsatzgruppen killed their victims—men, women, and children—by gathering them in ravines, mines, quarries, ditches, or pits dug specifically for this purpose. Jews were forced to hand over their possessions and remove their clothing, and were then shot. Their bodies were thrown into the ditches.  The commanders would file daily reports of these activities.
The constant up-close contact with murder had a terribly destructive effect on the Einsatzgruppen members. This led the Nazis to search for other execution alternatives. Soon the Einsatzgruppen were provided with gas vans for the murder of the remaining Jews.
After the war, leaders of the Einsatzgruppen were tried at Nuremberg and at later trials. Of 24 defendants, 14 were sentenced to death. Only four were actually executed; the rest received reduced sentences.