According to our criminal justice system, criminals should receive penalties that are proportionate to the severity of their crimes. Because serial killers commit the most bizarre and hideous crimes, they should receive the ultimate punishment according to this principle. However, not all serial killers get arrested since they carefully plan out their crimes. Those that get arrested and charged with murder do not always receive death sentences. The purpose of this research paper is to investigate and inform about the nature of serial murder and its punishments by using qualitative data from existing documents and surveys. Based on psychological and legal analysis of serial murders, this thesis provides reasons supporting and opposing the death penalty in serial murder cases.