June 11 – Wembley Stadium hosts a concert featuring stars from the fields of music, comedy and film, in celebration of the 70th birthday of imprisoned ANC leader Nelson Mandela.
June 14 – A small wildfire starts in Montana just north of the boundary for Yellowstone National Park. The Storm Creek fire expands into the park, then merges with dozens of other drought-inspired fires. Eventually, over 750,000 acres (3,000 km2) of Yellowstone – 36% of the park's area – burns before firefighters gain control in late September.
The Piper Alpha production platform in the North Sea is destroyed by explosions and fires, killing 165 oil workers and 2 rescue mariners. 61 workers survive.
Syringe Tide: the first reported medical waste on beaches in the Greater New York area (including hypodermic needles and syringes possibly infected with the AIDS virus) washes ashore on Long Island. Subsequent medical waste discoveries on beaches in Coney Island, Brooklyn and in Monmouth County, New Jersey force the closure of numerous New York–area beaches in the middle of one of the hottest summers on record in the American Northeast.
Singing Revolution: The Supreme Soviet of the Estonian SSR adopts the Estonian Sovereignty Declaration in which the laws of the Estonian SSR are declared supreme over those of the Soviet Union. The USSR declares it unconstitutional on 26 November. It is the first declaration of sovereignty from Moscow of any Soviet or Eastern Block entity.
The U.S. Drought of 1988 causes big crop damage in many states, impacts many portions of the United States and causes around $60 billion in damage. Multiple regions suffer in the conditions. Heat waves cause 4,800 to 17,000 excess deaths while scorching many areas of the United States during 1988.