January 31 - James Van Allen discovers the Van Allen radiation belt.
February 1 - Merger of Egypt and Syria to form the United Arab Republic, which lasted until 1961.
February 3 - Founding of the Benelux Economic Union, creating a testing ground for a later European Economic Community.
February 5 - Gamel Abdel Nasser is nominated to be the first president of the United Arab Republic.
February 5 - A hydrogen bomb known as the Tybee Bomb is lost by the US Air Force off the coast of Savannah, Georgia, never to be recovered.
February 6 - Eight Manchester United players are killed in the Munich air disaster.
February 21 - The Peace symbol is designed and completed by Gerald Holtom, commissioned by Campaign for Nuclear Disarmament, in protest against the Atomic Weapons Research Establishment.
February 22 - Egypt and Syria join to form the United Arab Republic.
February 23 - Cuban rebels kidnap 5-time world driving champion Juan Manuel Fangio.
March 1 - Samuel Alphonsus Stritch, is appointed Pro-Prefect of the Propagation of Faith and thus becomes the first American member of the Roman Curia.
March 1 - Turkish passenger ship Uskudar capsized and sank at Izmit Bay, Kocaeli, Turkey, killing at least 300.
March 3 - Nuri as-Said becomes the prime minister of Iraq for the 14th time.
March 5 - The Guangxi Zhuang Autonomous Region is established.
March 5 - Explorer 2 spacecraft launches and fails to reach Earth orbit.
March 16 - The Ford Motor Company produces its 50 millionth automobile, the Thunderbird, averaging almost a million cars a year since the company's founding.
March 17 - The United States launches the Vanguard 1 satellite.
March 24 - Elvis Presley is officially inducted into the U.S.Army.
March 25 - Canada's Avro Arrow makes its first flight.
March 26 - The United States Army launches Explorer 3.
March 26 - The African Regroupment Party (PRA) is launched at a meeting in Paris.
March 27 - Nikita Khrushchev becomes Premier of the Soviet Union.
April 4 - The CND Peace Symbol displayed in public for the first time in London.
April 5 - Ripple Rock, an underwater threat to navigation in the Seymour Narrows in Canada is destroyed in one of the largest non-nuclear controlled explosions of the time.
April 13 - Van Cliburn is the first American to win the Chaikovsky Compettion in Moscow.
April 14 - The Soviet satellite Sputnik 2 falls from orbit after a mission duration of 162 days.
April 18 - A United States federal court rules that poet Ezra Pound is to be released from an insane asylum.
May 12 - A formal North American Aerospace Defense Command agreement is signed between the United States and Canada.
May 13 - During a visit to Caracas, Venezuela, Vice President Richard Nixon's car is attacked by anti-American demonstrators.
May 13 - May 1958 crisis: a group of French military officers lead a coup in Algiers, demanding that a government of national unity be formed with Charles de Gaulle at its head in order to defend French control of Algeria.
May 18 - An F-104 Starfighter sets a world speed record of 2,259.82 km/h (1,404.19 mph).
May 21 - United Kingdom Postmaster General Ernest Marples announces that from December, subscriber trunk dialling will be introduced in the Bristol area.
May 30 - Memorial Day: the remains of two unidentified American servicemen, killed in action during World War II and the Korean War respectively, are buried at the Tomb of the Unknown Soldier in Arlington National Cemetery.
June 1 - Charles de Gaulle is brought out of retirement to lead France by decree for six months.
June 9 - HM Queen Elizabeth II officially opens London Gatwick Airport, (LGW), Crawley, West Sussex, United Kingdom.
June 16 - Imre Nagy, Pál Maléter and other leaders of the 1956 Hungarian Uprising executed.
June 17 - The Ironworkers Memorial Second Narrows Crossing being built connecting Vancouver and North Vancouver, Canada, collapses into the Burrard Inlet, killing many of the ironworkers and injuring others.
June 17 - The Wooden Roller Coaster at Playland, which is in the Pacific National Exhibition, Vancouver, Canada opened, and is still open to this day
June 23 - The Dutch Reformed Church accepts women ministers.
July 1 - The Canadian Broadcasting Corporation links television broadcasting across Canada via microwave.
July 1 - Flooding of the St. Lawrence Seaway begins.
July 5 - First ascent of Gasherbrum I, 11th highest peak on the earth.
July 7 - President Dwight D. Eisenhower signs the Alaska Statehood Act into United States law.
July 9 - Lituya Bay is hit by a mega-tsunami. The wave was recorded at 524 meters high, making it the largest wave in history.
July 10 - Highest tsunami wave ever recorded at Lituya Bay, Alaska, at 524m high.
July 14 - Iraqi Revolution: in Iraq the monarchy is overthrown by popular forces lead by Abdul Karim Kassem, who becomes the nation's new leader.
July 25 - The African Regroupment Party (PRA) holds its first congress in Cotonou.
July 26 - Explorer program: Explorer 4 is launched.
July 28 - Lord Jellicoe makes his maiden speech in the House of Lords.
July 29 - U.S. President Dwight D. Eisenhower signs into law the National Aeronautics and Space Act, which creates the National Aeronautics and Space Administration (NASA).
August 3 - The nuclear submarine USS Nautilus travels beneath the Arctic ice cap.
August 6 - Australian runner Herb Elliot breaks the world record for the mile at the Morton Stadium in Dublin, with a time of 3:54.5.
August 18 - Vladimir Nabokov's controversial novel Lolita is published in the United States.
August 23 - Chinese Civil War: The Second Taiwan Strait crisis begins with the People's Liberation Army's bombardment of Quemoy.
August 29 - United States Air Force Academy opens in Colorado Springs, Colorado.
September 2 - U.S. Air Force C-130A-II is shot down by fighters over Yerevan, Armenia when it strays into Soviet airspace while conducting a sigint mission. All crew lost.
September 12 - Jack Kilby demonstrates the first integrated circuit.
September 14 - Two rockets designed by the German engineer Ernst Mohr, the first German post-war rockets, reach the upper atmosphere.
September 15 - A Central Railroad of New Jersey commuter train runs through an open drawbridge at the Newark Bay, killing 58.
September 28 - France ratifies a new Constitution of France; the French Fifth Republic is then formed upon the formal adoption of the new constitution on October 4. Guinea rejects the new constitution, voting for independence instead.
October 2 - Guinea declares its independence from France.
October 4 - Fifth Republic of France is established.
October 7 - President of Pakistan Iskander Mirza, with the support of General Ayub Khan and the army, suspends the 1956 constitution, imposes martial law, and cancels the elections scheduled for January 1959.
October 7 - The U.S. manned space-flight project is renamed Project Mercury.
October 11 - Pioneer program: NASA launches the lunar probe Pioneer 1 (the probe falls back to Earth and burns up).
October 13 - Burial of Eugenio Pacelli, Pope Pius XII on the 41st anniversary of the "Miracle of the Sun".
October 13 - Michael Bond publishes the first story on Paddington Bear.
October 14 - The U.S. conducts an underground nuclear weapon test at the Nevada Test Site.
October 14 - The District of Columbia Bar Association votes to accept black Americans as members.
October 23 - The Smurfs, a fictional race of blue dwarves later popularized in a Hanna-Barbera animated cartoon series appear for the first time, in the story Le flute à six schtroumpfs, a Johan and Peewit adventure by Peyo which is serialized in the weekly comics magazine Spirou
October 26 - Pan American Airways makes the first commercial flight of the Boeing 707 from New York City to Paris, France.
October 27 - Iskander Mirza, the first President of Pakistan, is deposed in a bloodless coup d'état by General Ayub Khan, who had been appointed the enforcer of martial law by Mirza 20 days earlier.
November 10 - The Hope Diamond is donated to the Smithsonian Institution by New York diamond merchant Harry Winston.
November 25 - French Sudan gains autonomy as a self-governing member of the French Community.
November 28 - Chad, the Republic of the Congo, and Gabon become autonomous republics within the French Community.
December 1 - Central African Republic becomes independent from France.
December 1 - The Our Lady of the Angels School Fire in Chicago, Illinois kills 92 children and three nuns.
December 4 - Dahomey (present-day Benin) becomes a self-governing country within the French Community.
December 5 - Subscriber Trunk Dialling (STD) is inaugurated in the UK by Queen Elizabeth II when she speaks to the Lord Provost in a call from Bristol to Edinburgh.
December 5 - The Preston bypass, the UK's first stretch of motorway, opens to traffic for the first time. It is now part of the M6 and M55 motorways.
December 9 - Red Scare: The John Birch Society was founded in the United States.
December 11 - Upper Volta gains self-government from France, and becomes an autonomous republic in the French Community.
December 14 - The 3rd Soviet Antarctic Expedition becomes the first expedition to reach The Pole of Relative Inaccessibility in the Antarctic.
December 21 - French presidential election: Charles de Gaulle is elected President of France as his Union des Démocrates pour la République party gain 78.5% of the vote.
December 23 - Dedication of Tokyo Tower, world's highest self-supporting iron tower.
