The Game Boy Advance is useful in the modern era for more than watching Christopher Nolan blockbusters. Gizmodo notes that tinkerer Rodrigo Alfonso has Nintendo's 20-year-old handheld running PlayStation (and Genesis, and SNES) games without special modifications. The trick, as you might imagine revolves around a custom cartridge — you're technically running the game on a separate system.
The cartridge houses a Raspberry Pi 3 mini-computer running the RetroPie emulator and streaming both video and input through the GBA's multiplayer-oriented Link Port. Yes, that's constraining as you think it is — you can't transfer more than 1.6Mbps bi-directionally, and the Pi has to routinely give the "poor" GBA's processor a break for a few microseconds. Alfonso suggests lowering the stream resolution from the console's native 240 x 160 if a high frame rate is important.
Still, the results are mostly impressive. The special cart can handle classics like the Crash Bandicoot series and Spyro the Dragon at smooth frame rates, albeit with some video artifacts that reflect the limited bandwidth. You can overclock the GBA's processor to improve the frame rate and quality.
You'll have to build the cartridge and load code yourself, although Alfonso has helpfully provided both on GitHub. This probably won't replace a PSP if you want the most authentic PlayStation handheld experience you can get. It might, however, give you a reason to dig your GBA out of the closet.