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Following an attack by light bombers of the exile air force, launched from Nicaragua on Cuban airfields, the main assault on the Bay of Pigs began. The failure of the air attack to destroy the Cuban air force resulted in the surviving planes wreaking havoc on the counter-revolutionary invasion force and their air support. Fighting continued, as a 20,000 strong Cuban force repulsed the invading troops, leading to the collapse of the attack on 19th April.
The failed invasion caused a rapid deterioration of diplomatic relations between the U.S. and Cuban governments, which worsened during the Cuban Missile Crisis of the following year, and have improved little in successive decades.
To find out more about the Bay of Pigs Invasion, read the original New York Times report on the attack, and the article about the invasion on the JFK Library and Museum web site.