Everyone's favourite American trainer company was founded under the name 'Blue Ribbon Sports' in 1964. The famous 'swoosh' logo appeared in 1971 while the actual Nike brand name didn't follow until 1978.
Their 'Waffle' design came about when head honcho Bill Bowerman had the brainwave to fill his wife's waffle iron with liquid urethane. That's not a euphemism by the way. From that point on, Nike rose to prominence thanks to a procession of iconic, enduring designs.