April: Unemployment in Detroit reaches 20%, marking the height of the Recession of 1958 in the United States.
April 1: The BBC Radiophonic Workshop is established.
April 3: Castro's revolutionary army begins its attacks on Havana.
April 4 - April 7: In the first protest march for the Campaign for Nuclear Disarmament from Hyde Park, London to Aldermaston, Berkshire, demonstrators demand the banning of nuclear weapons.
April 4: Cheryl Crane, daughter of actress Lana Turner, fatally stabs her mother's gangster lover Johnny Stompanato (the stabbing is eventually ruled as self-defense).
April 6: Soraya Esfandiary Bakhtiari divorces the Shah of Iran, Mohammad Reza Pahlavi after she is unable to produce any children.
April 14: The satellite Sputnik 2 disintegrates in space after several orbits. - Van Cliburn wins the Tchaikovsky International Competition for pianists in Moscow, breaking Cold War tensions.
April 15: The San Francisco Giants beat the Los Angeles Dodgers 8-0 at San Francisco's Seals Stadium, in the first Major League Baseball regular season game ever played in California.
April 17: King Baudouin of Belgium officially opens the World Fair in Brussels, also known as Expo '58. The Atomium forms the centrepiece.
April 20: Montreal Canadiens win the Stanley cup after a defeating the Boston Bruins in 6 games.
April 21: United Airlines Flight 736 is involved in a mid-air collision with a U.S. Air Force F-100F-5-NA Super Sabre jet fighter near Las Vegas, Nevada. All 49 persons in both aircraft are killed. (source: Wikipedia)