You *could* build a receiver for GHz ranges... hams have been doing this for a while now. I'm building some 24 GHz transcievers right now in fact. Remember the Gemini & Apollo space missions? Hams were building receivers and dish antennae to listen to the (IIRC) 2.2 GHz signals from the space craft, even back then.
Today, very few analogue narrowband signals remain in the GHz range, so 'scanners' as you know them wouldn't translate all that well to the GHz ranges. Most signals up there are now wideband, very wideband! From a few hundred kHz wide to even tens or hundreds of MHz wide. Pretty much everything is digital modulation too. This means that, to a large degree, custom built receivers & demodulators are needed to receive anything. Another complication is that signals are generally transmitted with highly directional antennae, and you'd need to pretty close to directly in line of the transmitted signal to receive much.
Its radio scanning, Jim, but not as we know it.