Handheld players never went away entirely, but mostly languished until Nintendo came up with a spectacularly winning formula in 2001. The first ones were dedicated to playing a single game a popular early example was Mattel's Football, introduced in 1977.
Handheld game players had been around for decades. The PSP, a combination game system and media player, wasn't the most popular handheld system, but it was a crackling cauldron of surprisingly advanced tech for its time. The PlayStation Portable (PSP) was the labradoodle of the electronic games industry, an odd crossbreed, muscular and fun, but also kind of pricey.