How can I turn on a PC remotely?

I am using Team Viewer to control my PCs remotely. It lets me restart my PC, and this is a good feature.

Is it possible however to remotely turn a PC on which is already off (as in powered down)? Assume that all components of the PC are plugged in and the router is on.

All I can think of is something like sending a signal to the systems BIOS.

What you are looking for is Wake on LAN.

But Wake on lan will (probably) not work if your computer is behind a router/firewall. To get it to work you have to have open ports in your firewall to let the message through and send it towards your computer.

One way to get around this is if you have access to a computer behind your firewall that is always on and send your WOL-signal from that computer.

Hardware devices exist as well. Normally these are found in server room/datacenter environments in the form of PDUs, I did come across a single port one. There may be others out there as well.

Dataprobe iBoot

Also servers frequently will have remote management devices such as Dell's DRAC cards that also allow control of power.