There is no one right answer. What robots use is extremely varied. NASA for example: Curiosity (rover) - Wikipedia scroll down to computers.
I went to college for electronic engineering from 91-95 and learned of MIT's work ($ from NASA grants) just before then from a magazine article
http://www.ai.mit.edu/projects/hannibal/hannibal.html
I can't recall what they were using back then but there are a lot more options available today. I ended up going the IT route after college so I just dabble with electronics/robotics at home now and then.
A place to see some of what is used professionally is Microcontrollers - Page 1
From what I can gather the Arduino's, Pi's etc are looked upon by a lot as toys by a lot* but if you learn the Atmel mcu and can use it then your "professional". Which seems like a good stepping stone since the 'real world' uses the same MCU just not running the Ardiuno software. PIC is the other biggie, I started learning it in college using Parallax's toolchain and more recently picked up a Pickit 3 and have been getting back into PIC as I saved a couple of my old PIC designs, maybe I'll get to see if they actually work.
There are others but Pic and Atmel are the two biggest. Then going up from the MCU level you have the ARM (as used in the Beaglebone, Pi, etc) and x86 as well as some other specialized, those tend to be Linux/BSD or a real time OS or one of the specialized robot OS's. I'd bet that any modern robot has a network of multiple MCU's and/or CPU's just like any other modern complex product (car, airplane, etc).
- I should say that's is somewhat controversial as you will get some professionals who will defend the use of Arduino/Pi's in their design/products.