About as far away from vintage radio as you can get.
I have read about a single chip radio being available in several formats and the purchase of a new clock radio, clearly using one, stirred my interest. This started some research and I was amazed at the results I found, ending with purchase of a functional radio, described here.
The unit was described as a soldering practice board and came with 2 chips, a small number of discrete parts, a 4 digit display and a small circuit board. It was also offered in constructed form, which is what I bought.
As it referred to soldering practice, I thought there was a possibility that the chips may be duds, but powered it up with headphones connected and the display showed 88.0 and noise in the phones.
There are 5 push button switches, Power, Program+, Program-, Volume+, Volume- and pressing Program+ started a scan up to the first station detected and music in my ears. Everything functions in exactly the same way as my new clock radio, so it is a fully functional FM stereo radio.
One chip is the radio, the other is the driver for the display. These together with the PCB, a battery holder, switches, phones socket and the other components came to $7.22.
The inner workings of the chip are beyond this forum, other than there is a mix of analogue RF circuits and digital signal processing.
This has been a very interesting experience, with an entire radio reduced to a single component.
Harold

This is pretty much how digital radios work, with the exception that there is also a station finder button which, when pressed, will make the radio download tuning details for all the available stations before letting the user do any tuning. Two of the chips inside that radio were permanently attached to the board, looking like blood blisters and all the pins also behind the plastic moulding.

Nothing to fix on them unfortunately, so when they break, it's in the bin.

Photos uploaded.