In October 1939 Hitler signed a "euthanasia decree" backdated to 1 September 1939 that authorized Reichsleiter Philipp Bouhler, the chief of Hitler's Chancellery, and Karl Brandt, Hitler's personal physician, to carry out a program of involuntary "euthanasia"; after the war this program was named Aktion T4.[98] It was named after Tiergartenstraße 4, the address of a villa in the Berlin borough of Tiergarten, where the various organizations involved were headquartered.[99] T4 was mainly directed at adults, but the "euthanasia" of children was also carried out.[100] Between 1939 and 1941, 80,000 to 100,000 mentally ill adults in institutions were killed, as were 5,000 children and 1,000 Jews, also in institutions. In addition there were specialized killing centres, where the deaths were estimated at 20,000, according to Georg Renno, the deputy director of Schloss Hartheim, one of the "euthanasia" centers, or 400,000, according to Frank Zeireis, the commandant of the Mauthausen concentration camp.[101] Overall, the number of mentally and physically handicapped murdered was about 150,000.[102]
Several scholars have suggested that the Final Solution began in the newly formed district of Bezirk Bialystok.[48] The German army took over Białystok within days. On Friday, 27 June 1941, the Reserve Police Battalion 309 arrived in the city and set the Great Synagogue on fire with hundreds of Jewish men locked inside.[49] The burning of the synagogue was followed by a frenzy of killings both inside the homes around the Jewish neighbourhood of Chanajki, and in the city park, lasting until night time.[50] The next day, some 30 wagons of dead bodies were taken to mass graves. As noted by Browning, the killings were led by a commander "who correctly intuited and anticipated the wishes of his Führer" without direct orders.[49] For reasons unknown, the number of victims in the official report by Major Weis was cut in half.[50] The next mass shooting of Polish Jews within the newly formed Reichskommissariat Ostland took place in two days of 5–7 August in occupied Pińsk, where over 12,000 Jews died at the hands of Waffen SS,[51] not the Einsatzgruppen.[41] An additional 17,000 Jews perished there in a ghetto uprising crushed a year later with the aid of Belarusian Auxiliary Police.[52]

Many Jews attempted to flee Germany, and thousands succeeded by immigrating to such countries as Belgium, Czechoslovakia, England, France and Holland. It was much more difficult to get out of Europe. Jews encountered stiff immigration quotas in most of the world's countries. Even if they obtained the necessary documents, they often had to wait months or years before leaving. Many families out of desperation sent their children first.
Historians of the Holocaust are divided into two schools: the “intentionalists” insist on the central role of Nazi ideology and believe that there was a carefully prepared plan for the extermination of European Jewry; the “functionalists” or “structuralists” by contrast, stress the chaotic nature of the Nazi system, a non-design reflected in their foreign and economic policies as well. According to the latter school, it was this inherent disorder rather than premeditated design that led, through a process of cumulative radicalization, to the systematic extermination of European Jewry.
Raphael Lemkin, a holocaust survivor who worked on the Nuremberg Trials, coined the term genocide and spent 4 years pushing for it to be added to international law. As Champetier de Ribes, the French Prosecutor at the Nuremberg Trials explained “This [was] a crime so monstrous, so undreamt of in history throughout the Christian era up to the birth of Hitlerism that the term ‘genocide’ has had to be coined to define it.” Ultimately, in 1948 The United Nations Convention on the Prevention and Punishment of Genocide was adopted, and it entered into force in 1951. The convention defined genocide in legal terms based on Lemkin’s work, and is the basis for genocide prevention efforts today.
In most ghettos, Nazis ordered the Jews to establish a Judenrat (Jewish council) to administer Nazi demands and to regulate the internal life of the ghetto. The Nazis routinely ordered deportations from the ghettos. In some of the large ghettos, 1,000 people per day were sent by rail to concentration and extermination camps. To get them to cooperate, the Nazis told the Jews they were being transported elsewhere for labor.

In June 1941, Mengele was posted to Ukraine, where he was awarded the Iron Cross 2nd Class. In January 1942, he joined the 5th SS Panzer Division Wiking as a battalion medical officer. After rescuing two German soldiers from a burning tank, he was decorated with the Iron Cross 1st Class, the Wound Badge in Black, and the Medal for the Care of the German People. He was declared unfit for further active service in mid-1942, when he was seriously wounded in action near Rostov-on-Don. Following his recovery, he was transferred to the headquarters of the SS Race and Settlement Main Office in Berlin, at which point he resumed his association with von Verschuer, who was now director of the Kaiser Wilhelm Institute of Anthropology, Human Heredity, and Eugenics. Mengele was promoted to the rank of SS-Hauptsturmführer (captain) in April 1943.[20][21][22]