The discovery of natural radioactivity by Antoine Henri Becquerel and the most significant contributions of Marie Curie and Pierre Curie towards radioactivity are described. Types of radiations emitted by a radioactive element and the theories and laws governing their emission are presented. The discovery of important phenomena such as artificial radioactivity and transmutation of elements are discussed. The phenomenon of nuclear fission and its proposed theories are described. A very brief description of the Manhattan Project for producing atomic bomb during World War II is given and in this process the first nuclear reactor was created by Enrico Fermi. The improvements in the designs of nuclear reactors and energy produced in the controlled nuclear fission process for producing electricity is explained. This chapter also includes a brief description on nuclear fusion: the proton-proton cycle and the formation of hydrogen bomb. Ongoing global efforts toward controlled nuclear fusion for peaceful energy production are also highlighted.