Most Routers & Switches and Smart TV's for home use are using embedded Linux to operate the peripherals, flash memory with OS and RAM, There will be a kernel boot loader, OS and facility to update the OS as well as parameter tables using whatever serial ports are available. Ethernet, USB etc.
They are also used for GPS touchpads, Medical devices, In-Flight Entertainment systems , portable web TV boxes, Smart Phones and PDA's to name a few more examples.
They started as standalone fast booting systems without displays to serve specific functions and now have expanded into full featured systems using special lower cost, energy efficient single , dual and quad core processors like Qualcomm's unlike the AMD compatible x64 architectures used in PC's 50~250W CPU/GPU"s but they can be compiled for a wide range of processors.
They also are distinct with having no royalties or licensing fees; a stable kernel; and the source code can be modified at will but the driver framework tends to be relatively complex..
If you have specific safety-critical specifications you must meet, embedded Linux might not be your best bet But it may not be a good choice, if you have Real Time hard coded periodic high frequency routines that cannot fail, then you would use an RTOS type instead. Router functions are high speed but asynchronous in the application layer.