The first Sony portable CD player (which eventually would be the Discman in the years to come) came out sometime in 1984. Known as the CD Walkman in some parts of the world (read Japan), the Discman soon became a rage in the 90s.
The Sony Discman still lives. The last one came out in 2011. It has been rebranded under the Walkman tag and supports MP3 playback.