Berlin Olympic Games took place in 1936, during the Nazi government. Hitler took the opportunity to promote his political ideas and prohibited Jews from participating. After other nations threatened with not participating he allowed foreign athletes from other ethinicities to participate.
Munich Olympic Games in 1972 were interrupted by the Munich Massacre. 11 members of the Israeli olympic team were killed by the Palestinian terrorist group known as Black September.
Beijing Olympic Games were organized in 2008. The main controversies were related to freedom of press and to the complaints of foreign journalists with the restrictions imposed by the Chinese goverment.
Mexico City Olympic Games took place in 1968. There were controversies regarding the participation of segregationist South Africa. Many African American athletes threatened with not participating if South Africa was invited. There was also the Tlatelolco massacre when a student protest, which aimed to took profit of the international visibility during the Olympic, was repressed.
Moscow Olympic Games took place in 1980, in the capital of the Soviet Union during the Cold War era. Only 80 nations participated, the smallest number of participants ever. This boyccot was promoted by the US and 66 countries followed it because of the Soviet invasion of Afghanistan.
Los Angeles Olympics were celebrated in 1932, during the Great Depression. Many athletes and teams could not pay the transportation to Los Angeles, and less participants could come than in the previous edition.