June 1: The BBC transmits a coded message (the first line of the poem "Chanson d'automne" by Paul Verlaine) to the French Resistance, warning that the invasion of Europe is imminent. - Two K-class blimps of the United States Navy complete the first transatlantic crossing by non-rigid airships, from the U.S. to French Morocco with two stops.
June 2: The provisional French government is established.
June 4: Rome falls to the Allies, the first Axis capital to fall. - A hunter-killer group of the United States Navy captures the German submarine U-505, marking the first time a U.S. Navy vessel has captured an enemy vessel at sea since the 19th century.
June 5: The German navy's Enigma messages are decoded almost in real time. - British Group Captain James Stagg correctly forecasts a brief improvement in weather conditions over the English Channel which will permit the following day's Normandy landings to take place (having been deferred from today due to unfavourable weather). - At 10:15 p.m. local time, the BBC transmits the second line of the Paul Verlaine poem to the French Resistance, indicating that the invasion of Europe is about to begin. - More than 1,000 British bombers drop 5,000 tons of bombs on German gun batteries on the Normandy coast in preparation for D-Day. - US and British paratrooper divisions jump over Normandy, in preparation for D-Day, including 82nd and 101st Airborne divisions of the United States.
June 6: D-Day for the Normandy landings: 155,000 Allied troops shipped from England land on the beaches of Normandy in northern France, beginning Operation Overlord and the Invasion of Normandy. The Allied soldiers quickly break through the Atlantic Wall and push inland, in the largest amphibious military operation in history. This operation helps liberate France from Germany, and also weakens the Nazi hold on Europe.
June 7: The steamer Danae (Greek: ?????) carrying 350 Cretan Jews and 250 Cretans on the first leg of their way to Auschwitz is sunk without survivors off Santorini. - Bayeux is liberated by British troops.
June 9: Soviet leader Joseph Stalin launches the Vyborg-Petrozavodsk Offensive against Finland, with the intent of defeating Finland before pushing for Berlin.
June 10: 642 men, women and children are killed in the Oradour-sur-Glane Massacre in France.
June 13: Germany launches the first V-1 Flying Bomb attack on London.
June 15: Battle of Saipan: United States forces land on Saipan.
June 17: Iceland declares full independence from Denmark.
June 19: A severe storm badly damages the Mulberry harbours on the Normandy coast.
June 22: Operation Bagration: A general attack by Soviet forces clears the German forces from Belarus, resulting in the destruction of German Army Group Centre, possibly the greatest defeat of the Wehrmacht during WWII. - Burma Campaign: The Battle of Kohima ends in a British victory.
June 25: The Battle of Tali-Ihantala (the largest battle ever in the Nordic countries) begins between Finnish and Soviet troops. Finland is able to resist the attack and thus manages to stay as an independent nation.
June 26: American troops enter Cherbourg.
June 29: The Holocaust - The deportation of Hungarian Jews to Auschwitz and other Nazi concentration camps begins. (source: Wikipedia)