Robotic applications take many forms, but much of the time it comes down to creatively controlling servo motors. If you’d like to control up to 16 servos over WiFi, here’s a solution called the WiFinch. It’s board allows you to control servos via WiFi using an Android app, or you can reconfigure it using Arduino, NodeMCU, or MicroPython. You can see it below controlling a robotic arm via a smartphone.
It can also control electronic speed controllers (ESCs) or any other device compatible with a digital servo signal, so there are certainly quite a few interesting possibilities.
If you’re sure you’re going to build a robot with this device, or just want a few accessories to go along with the board, you could also step up to their “Robot Maker Kit” featuring 5 servos, a battery holder, and a USB cable. Though you could certainly find a use for those components, if you need some ideas, Rototeurs has you covers with their “Printabots” designs.