There may be more than two million apps in Google Play, that does not mean that you will always find what you are looking for. While Google's own app store is the easiest way to download apps for your Android smartphone or tablet, there's another way: through APK files.
APK stands for Android Package. They are archive files, similar to zip or JAR files, that contain the code of an app. You can use those files to put apps on your Android device that are not (yet) included in Google Play.
Danger
Let's start with the most important thing: there is a dangerous side to downloading apps outside of Google Play. APK files can contain malware or viruses, and it is certainly not said that they do exactly what they say they do. Nor can you rely on your data being treated securely.
Google approves all apps that end up in Google Play, so that the risk of the above dangers is very small. That is not always the case with APK files that you get from the internet. So make sure you know what you're getting and be careful when disclosing personal information in the app.
APKMirror
That said, there is a website that basically doesn't have malware-containing files. That site is APKMirror, and is a collection of apps that are not in Google Play, or beta versions of well-known apps such as WhatsApp or Facebook. APKMirror checks the apps for authenticity and whether they are uploaded by the official creator of the app. At least that's how you know almost make sure you don't get malicious software.
To download APK files, go to apkmirror.com on your Android device. There you will find a long list of apps that have recently been released or updated. At the top right you will find a search function, which you can use if you already know which app you want.
Download APK files
In order to download APK files, you must first ensure that your smartphone or tablet can access files outside of Google Play. To do that go to Settings > Security and check under the tab Device Manager the option Unknown sources at. Your device will no longer sulk when you try to download an unknown file.
Go back to apkmirror.com, find the app you want and press it for more information. Scroll down and press Download APK. You can also press the download button (the down arrow) directly in the search results list. You will now see another warning because you are trying to download a file from an unknown source. Press OK and the file is downloaded.
Then open the Downloads folder on your device and tap on the file you just downloaded (or use the message center). On the next screen, press to install, after accepting any new permissions. The app will now be installed on your device. Beta versions are placed on your smartphone as a separate app, so you can still use the older, official version.
Other Resources
Besides APKMirror, there are countless other sources that offer APK files. However, not all of them are equally safe. Some well-known sites that do not have official apps in Google Play offer APK files on their website. For example, gambling websites may still have an app, even if you cannot download it via the official channels.
Other well-known APK sites are apkfiles.com and android-apk.org. Both are generally safe, but as a result, the range is also somewhat limited. Often the best way is to do a Google search for apk download [app name] to do. In those cases, however, you have to be very careful where you get the file from. To be on the safe side, make sure you also have a good backup of your device or files, in case you do get malware. And as always applies when downloading files: use your common sense.