During the Holocaust, children were extra vulnerable as victims. The Nazis were on a mission to eradicate dangerous or 'unwanted' groups based on a variety of ideological views, class statuses, religions, races, and other elements. Because children were essentially of no value to Nazi society, they were regularly killed. Children who were old enough to work were often put into forced labor where they could be put to use. Some were used for torture or medical experimentation. Older children had better survival rates because they could be used in labor, but no child that wasn't part of the 'Master Race' in Nazi Germany was safe from potential imprisonment or death.
There were a few different fates for children of the Holocaust. Some were killed at death camps or killing centers. Others were killed immediately upon birth or in institutions, or during reprisal operations that occurred under the Nazi regime. Some children born in ghettos or camps were able to survive because they were hidden by prisoners. Many children over the age of 12 were used for labor or medical experimentation, which meant that some died and some lived as a result of their use. Of course, there were also thousands of children who died from starvation, exposure, and disease in ghettos, during transport to camps, and once they arrived at camps if they weren't immediately sent to death.
The Nazis killed more than 1.5 million children in total, including Jewish children, gypsy children, Polish children, Soviet children, and German children who had mental or physical disabilities that ultimately rendered them 'useless' the Nazi regime. Children were often first in line for death if they didn't die of other causes, along with the elderly, disabled, and ill, and were first led to mass graves to be shot or into gas chambers once the Nazis started using gas a means of more effective extermination.
The gas chambers not only expedited killing, but it supposedly saved the Nazis the 'mental anguish' of killing them by shooting. Of course, that doesn't mean that thousands of children weren't shot and killed during the Holocaust. Many children that were fitting for the "Master Race" were kidnapped and taken to the Third Reich for adoption by German families if they could be 'Germanized' according to Nazi standards. There were thousands of orphaned children at the end of World War II, and were put into displaced persons camps before being emigrated to countries like Israel.