WhatsApp is going to stop supporting many phones with a new software update that is rolling out. One of the main OSs being affected is Windows based phones. WhatsApp has said on their FAQ page that after 31st December, "WhatsApp will no longer support Windows Phone operating systems". That's one way to wish people a happy new year. As well as this, WhatsApp might not be available in the Microsoft Store by July 1st 2020.
The other major OS's are iOS and Android. To have WhatsApp running on an iOS device, you must have iOS 9 or higher. iPhones that support iOS 9 is the iPhone 4s, iPhone 5, iPhone 5c, iPhone 5s, iPhone 6, and finally the iPhone 6 Plus. If you have iOS 8, however, you'll still be able to use your account until 1st February. With iOS 8 you can't create new accounts or reverify existing accounts though.
To have WhatsApp running on an Android, you must have Android version 3.0 above. This that Android version 2.3.7 (Gingerbread) and lower aren't going to be supported by the time February comes around. Yes, like the iPhones, you'll be able to use WhatsApp on an already existing account but only until February.
So, the Android phones from the last decade are safe!
There is no news at present if WhatsApp is going to stop supporting Tizen devices, such as the Samsung Z1, Z2, Z3, and Z4. Most likely, WhatsApp for Tizen users is going to come to an end but there is no official news as of yet. We will keep you updated when we hear something.
The WhatsApp app is being updated and is blocking certain mobile operating system, such as Windows mobile and most likely Tizen. They are are also limiting certain OS versions due to the fact they want to ensure user security. Not a completely bad reason :).
If you're going to end up losing support, you can either backup or export your chats so you can keep em for a bit longer or restore them on your new phone.