Short answers, pulled from the story.
Contemporary history is a subset of modern history covering the period from about 1945 to the present. In English-language historiography it describes the era still close to the present, and in the social sciences it runs alongside the rise of postmodernity.
The Cold War was the central political confrontation of contemporary history, lasting from 1947 to 1991 between the Western Bloc led by the United States and the Eastern Bloc led by the Soviet Union. It spurred fears of nuclear war and proxy conflicts, but an all-out hot war was avoided. It ended with the Revolutions of 1989 and the dissolution of the Soviet Union on the 26th of December 1991.
Decolonization was the most important development across Southeast Asia and Africa from 1946 to 1975, as the British, French, Dutch, and Portuguese colonial empires were dismantled. British India gained independence in 1947 and was partitioned into India and Pakistan, while conflicts such as the Algerian War from 1954 to 1962 and the Portuguese Colonial War from 1961 to 1974 marked the end of European rule.
Living standards rose sharply across the developed world during a post-war economic boom that France called Les Trente Glorieuses. West Germany recovered with the wirtschaftswunder, Japan became the second largest economy in 1968, and the United States and the dollar displaced the UK at the center of the world economy in an era sometimes called Pax Americana.
After 1945 science advanced in spaceflight, nuclear technology, lasers, semiconductors, genetics, and particle physics. The United States landed Apollo 11 on the Moon in 1969, the Mars Science Laboratory Curiosity landed on Mars on the 6th of August 2012, and in 2012 European physicists demonstrated the existence of the Higgs boson.
The Cold War ended through a peaceful chain reaction beginning with the Pan-European Picnic in 1989 and the fall of the Berlin Wall. The Revolutions of 1989 toppled Eastern Europe's communist governments, and the Malta Summit, the failed August Coup, and the formal dissolution of the Soviet Union on the 26th of December 1991 sealed its end.
Contemporary history saw the rise of English as a global lingua franca, growing urbanization, the sexual revolution after the pill was approved in 1960, and the spread of television, Hollywood film, and the Internet. The Information Age brought the first commercial computers and the Internet, connecting the world in new ways.