The most obvious effect was the increasing movement of anti-colonialism and the eventual end of the French, British and Dutch empires. The rise of nationalism was a natural result of the political philosophies of Europe being taken seriously by the colonised. In Asia, this was also given impetus by the military victories won early in the Second World War by Japan, proving to Asian peoples that Europeans were not necessarily superior and that their rule could be challenged.
The rise of nationalism in these areas combined with the economic dislocation of Europe in the War led to a situation in which European powers did not have the money (and in some instances the will) to maintain overseas colonies. France lost control of their possessions in Indo-China during the war with the Viet Minh under Ho Chi Minh, a war fueled by nationalism and the ironic juxtaposition of communism and the political liberation theories of American writers such as Thomas Paine and Thomas Jefferson. In Africa, rising nationalism and communist aid gave rise to wars in Kenya, the Congo and other countries, and even when put down these led to an awareness on the part of European powers that the tide of history was against continued colonisation. Economic cooperation became far more attractive.
Wars and revolutions continued in Malaysia and other countries, along with peaceful protest and the entire range of nationalist beliefs, political ideologies and techniques of political agitation. The Dutch fought back in Indonesia but lost in 1950, and the war in Algeria immediately following the loss of Indo-China ended the French Empire. India's independance signaled the most significant victory of anti-colonial nationalism.
In the Middle East, European powers were not interested in fighting the local desires for independance. The potential rewards of economic exploitation of the oil fields (for both Europeans and locals) was far more attractive to all concerned than fighting.
In most areas of the world, attempts by European nations to maintain compliant governments in the former colonies did not work well. As to the theory behind these agitations and rebellions, the most important work is The Wretched of the Earth, by Fritz Fanon.