Your Smartphone is a FM radio reciever.

[Geek-9pm]

No, not Bluetooth.
No, not Internet.
A real analog FM receiver that picks up local FM stations over the air.
If you don' t already know this, it might be you cell phone company has removed the app that turns on the chip. (Why wood anybody do that?)

Read here:
How to Unlock the FM Radio Hidden on Your Smartphone

A large number of Android Phones use he same chip set. If yours is one of them, then you just need the right app to turn it on.
The quality can be very good on local stations. But the headphones must be attached to pick up enough signal.

Using the direct FM thing saves your data usage. No data connection misused. It is called Radio. Ask your parents. They remember.

My question. Why not AM radio also? 

[BC_Programmer]

The FM Radio is part of the more common SoC chips. They are typically disabled in hardware- you cannot enable them in any way, beyond, of course, hardware modifications. Part of the reason that aspect is disabled may be to conform to desired FCC/CRTC rulesets. That it is disabled by carriers wanted to cause people to use data so they can be charged for it is probable but unlikely- the Carriers do not control the hardware features of the phones they use. They could lock out an active FM Radio through software but most phones have the FM Radio functionality, if it is available at all, disabled even on devices that have never been associated with any carrier at all.

Why not AM radio also? 

As I'm sure you remember, The antenna (Radio Loop or Ferrite wound core) required to pick up AM radio is much bulkier than those that work for FM Radio, and AM Radio would require more shielding to prevent undesired interference from now-common sources like Fluorescent lights. That, and incredibly low demand for such a feature is likely why it is not on the integrated SoC that are used for mobile devices.

[Salmon Trout]

My ZTE Blade 3 (2011-2015) and my current Motorola Moto G (both UK models) have FM radio fully functional. Is this a US thing?

[BC_Programmer]

My ZTE Blade 3 (2011-2015) and my current Motorola Moto G (both UK models) have FM radio fully functional. Is this a US thing?

North America I think.

My Nexus 6 was unlocked and has never had any carrier but I cannot seem to access any Radio features of the SoC which from what I found does have a receiver. It could be related to a difference between FCC and/or CRTC rules and OfCom (The UK equivalent (?))) wit hregards to the rules on reception devices.

The Radio feature being enabled seems to depend on the country. It might actually be a feature of the board it is installed in (eg pin floating/grounded/powered/etc. turns it on or disables it or something so the smartphone boards in different countries differ in that detail)

[Salmon Trout]

A February 2018 story on The Verge says that Samsung is "unlocking" FM radio on upcoming phones. The article says that the FCC had asked Apple to activate the iPhone’s FM radio to aid public safety. Apple said the iPhone 7 and 8 models don’t have the chip, and that older phones already include other safety features. FCC chairman Ajit Pai, the Verge claimed. previously said that about 44 percent of the “top-selling smartphones” in the US had activated FM radios compared to 80 percent in Mexico.

https://www.theverge.com/2018/1/11/16877766/samsung-fm-radio-chip-nextradio-us-canada

[Geek-9pm]

Some things to clarify.
FM ratio on one IC is not new. In fact, there are a number of single chip solutions for both FM only and AM/FM. Some of these do work good on the short wave bands also.
(As to AM radio, lack of interest and the issue of ferrite core  stops development of a tiny AM/FM chip.)

As for cell phones, FM radio is a standard feature on Android devices. Most devices have the chip is some form. The earphone serves as the antenna, so the absence of a visible antenna does not mean there is no FM radio inside.

This topic has been of concern here in the USA. Look here:
https://www.npr.org/sections/alltechconsidered/2015/04/16/400178385/the-hidden-fm-radio-inside-your-pocket-and-why-you-cant-use-it
The National Association of Broadcasters has been asking mobile makers to change this. But the mobile industry, which profits from selling data to smartphone users, says that with the consumer's move toward mobile streaming apps, the demand for radio simply isn't there
Yes, 'tis a USA thing. 

You can check the Google Play store and find apps that will turn on the direct FM radio chip. It would take little effort to have this feature included in the standard carrier package. The hardware is already there.

...from NPR:
Most smartphone models come with a built-in FM feature. Samsung, Apple and LG are among those who have not switched on the chip, but HTC and Motorola chips haven't been blocked, Smulyan says. Sprint has turned on the FM chip for phones on its network.

[Salmon Trout]

FM ratio on one IC is not new.

The Philips TDA7000 came out in 1983. Initially the 2 Dutch guys at Philips who designed it could not get the company interested (they said it was impossible) so they had some samples made privately and showed them to Japanese clients, who asked to order one million chips. They went into everything - clocks, music players, novelties even. To date more than 5 billion have been sold. I made a radio on a breadboard in 1988 using one of these.

[glathem40]

Interesting.  I have a Samsung Galaxy J3 Emerge purchased about a year and half ago.  I live in New Mexico.  About a year ago I downloaded the NextRadio app.  When launched it  searches for local stations.  Upon selecting a station it tells you to plug in the earphones -It says they act as the FM antenna.  I use it when I go for a walk, but often find the reception sketchy - You have the option to stream the station.  When streaming the reception is flawless.  I always find it interesting to see how far away from my house my wifi is transmitting - there will be a second of silence as it switches from the cell to the wifi connection.  So I've always assumed I can listen to the radio 3 ways - Internal FM antenna, cell network and Wifi.

[Salmon Trout]

About a year ago I downloaded the NextRadio app.  When launched it  searches for local stations....So I've always assumed I can listen to the radio 3 ways - Internal FM antenna, cell network and Wifi.

This is puzzling to me, I wonder if we are talking about slightly different things, or maybe they do things differently over there? On both my smartphones, the FM radio appears as a native or built-in "app" option - it was there when the phone was new.The sleeve part of the audio jack is the antenna connector. You can get antenna wires with short connectors. In each case, the first time you use it, it offers to find stations and store them, on the display you can see it going from 88 MHz to 108 MHz. On the way, it finds stations of varying strengths, and if they are powerful enough you hear them in stereo. It also shows the RDS (RDBS in USA) info about the station, e.g. station name "BBC R4", and the current program title etc. You can store the stations and go to them by menu, or you can just press "up" and "down" on-screen buttons and it locks onto the stations it finds as you do that. If you are in a bus or walking about and the signal strength changes, you get all the FM radio type symptoms, hiss, garbled sound, etc. When a station is weak you can switch to mono to clarify. All this is just like the regular FM radio that I have in my kitchen, and like the ones in cars. I can do all of this with the phone in airplane mode, right now it is picking up BBC Radio 4 on 93.7 MHz in perfect stereo. So what I have is not dependent on the cell network, or wi-fi. It knows about the phone, because it mutes when a call comes in. I guess the SoC is running it.

[Geek-9pm]

Thank your for the details about the TDA7000 history. Amazing. 
Of course, that chip is  not part of the modern Smart Phone.

There are a number of old DITY projects using that old chip. You can search Google for old pages that are still out there.
Also, newer DIY kits for that kind of FM radio can be found on eBay. The kits are less that the cost of parts.

That kind chip uses a PLL to detect rhe audio content.ewer versions are suitable for stereo decoding of local FM stations.
https://en.wikipedia.org/wiki/Phase-locked_loop

But modern Smart Phones use digital decoding.

EDIT: Here is a You Tube thing that explains why you want a cell phone e in a disaster. Maybe that is why the FCC wants the FM radio to be enabled.
https://www.youtube.com/watch?v=5MJn5pI5XNw