What happens to children with childhood leukemias?

Usually they thrive. The cure rate for all childhood leukemias has improved tremendously over the past few decades, and much effort now is directed toward minimizing long term side effects, such as numbness, secondary cancers, or slowed mentation. A very reasonable goal today is for the child to be cured and lead a perfectly normal life.
Leumemia types. Definitely the out come depends on type of leukemia and how advanced the disease is at the time of diagnosis. The most common type is all (acute lymphoblastic leukemia), and in general these children would be treated with aggressive chemotherapy followed by maintenance treatment , the cure rate is above 90%.