The Einsatzgruppen were mobile killing squads. Heinrich Himmler and Reinhard Heydrich formed four small groups of murderers immediately before the Nazi invasion of the Soviet Union. They totaled about 3,000 men.
The Einsatzgruppen entered the Soviet Union behind the army, and murdered, mostly by shooting and gas vans, the undesirables: political "criminals", Polish governmental officials, gypsies and, mostly, Jews.
Jews were rounded up in every village, transported outside to a wooded area or a ravine (natural or constructed by Jews). They (men, women and children) were stripped, shot and buried. Their clothes were sent back to Germany.
Sachar provides a description of one of the most brutal mass exterminations - at a ravine named Babi Yar, near Kiev:
"Kiev ... contained a Jewish population of 175,000 on the eve of
the Nazi invasion of the Soviet Union in 1941. The Nazi forces
captured the city in mid-September; within less than a fortnight, on
the 29th. and 30th., nearly 34,000 Jews of the ghetto were brought to
a suburban ravine known as Babi Yar, near the Jewish Cemetery, where
men, women, and children were systematically machine-gunned in a
two-day orgy of execution. In subsequent months, most of the remaining
population was exterminated....
The riddled bodies were covered with thin layers of earth and the
next groups were ordered to lie over them, to be similarly dispatched.
To carry out the murder of 34,000 human beings in the space of two
days could not assure that all the victims had died. Hence there were
a few who survived and, though badly wounded, managed to crawl from
under the corpses and seek a hiding place....
After the main massacre, the site was converted into a more
permanent camp to which thousands of victims from other parts of the
Ukraine could be sent for extermination. It became known as the
Syrets camp, taking its name from a nearby Kiev neighborhood. Several hundred
selected prisoners were quartered there - carpenters, shoemakers,
tailors, and other artisans - to serve the needs of the SS men and
the Ukrainian guards. They were usually killed within a few weeks and
replaced by others who continued their duties. In charge of the
administration and ultimate killing was Paul von Radomski, who seemed
to crave a reputation for outdoing his sadist colleagues in other
(from Sachar, Abram L. The Redemption of the Unwanted, New York: St. Martin's/Marek, 1983).