The 1979‘sMilton-Bradley Microvision was the first globally hand-held cartridge-based system. The first hand-held was soon forgotten during the fall video game crash in early 1980s until the concept was reanimated ten years later, Nintendo GameBoy, became the one of still standing and successfully brand-name video game in history of portable video game.

Since Gameboy erupted, several companies across the globe follow the same formula: media storage (cartridges, flash or CD) to insert into the portable system to play the game, but uses different processor, physical, shape, resolution and function.

—Daveynin’s Thing Game Portable Family Tree (DFulmer.com)

See also a similar, but less comprehensive, chart describing the development of game controllers.