Wake-on-Lan
Bottom line: Wake-on-LAN is an Ethernet (wired) protocol so your target computer must be connected through an Ethernet cable to the router that hosts your Internet connection. The BIOS must be configured to enable WOL, and the operating system must be configured to enable it. The computer may only be able to wake from certain sleep states, not necessarily full power down. Finally, the system should be thoroughly tested before relying on it.
During a recent trip, I needed to access iTunes on my computer back home. Fortunately my spouse was at home and the computer was already running. As soon as I can get the correct length Ethernet cable I will just permanently connect my computer to the router.