Short answers, pulled from the story.
There were 15,754 documented victims of Nazi human experimentation, conducted mainly between 1942 and 1945. The true number is believed to be higher. About a quarter of documented victims were killed; most survivors suffered severe and permanent injuries.
The Doctors' Trial, formally titled USA vs. Karl Brandt et al., began on the 19th of August 1947. Allied forces prosecuted 23 doctors and administrators for conducting medical experiments on concentration camp prisoners. Several defendants argued that no international law prohibited such experimentation.
The Nuremberg Code is a set of ten principles governing ethical medical experimentation, drafted by American Medical Association representatives Leo Alexander and Andrew Conway Ivy during the Doctors' Trial. It requires voluntary consent, avoidance of unnecessary suffering, and a reasonable belief that experiments will not result in death or disability. Despite its influence, the Code was never incorporated into German or American medical law.
Josef Mengele conducted twin studies at Auschwitz in 1944, gathering 582 twins according to records cited by Paul Weindling. Prisoner anthropologists used precision instruments to measure limbs, head size, and other physical characteristics, and blood was regularly drawn for analysis. Mengele fled Auschwitz in December 1944 without ordering the twins to be killed.
The Dachau freezing experiments were conducted beginning in August 1942 by Sigmund Rascher, an SS doctor who reported directly to Reichsfuhrer-SS Heinrich Himmler. Prisoners were forced to sit in tanks of freezing water for up to three hours or were left naked outside in below-freezing temperatures. Rascher presented the findings at a 1942 medical conference titled Medical Problems Arising from Sea and Winter.
Data from the Nazi experiments has been used and considered for use in multiple fields, generating ongoing controversy. By 1984, at least 45 publications had cited the Dachau freezing experiments in research on hypothermia treatment. In 1990, Robert Berger concluded the Dachau data contained all the ingredients of scientific fraud; Arnold S. Relman, editor of The New England Journal of Medicine from 1977 to 1991, refused to publish any article citing Nazi experimental data.