As is usual with this type of application, with adAway, you can create a 'whitelist' of websites to which you can add exceptions if you want. Of course, you can also add more hosts to your blacklist if you want, too. But no matter what you decide to do, all the settings can be configured according to your preferences.
It is important to note that to use adAway, you'll need a rooted device. If your Android device is not rooted, you won't be able to access all the features described above. To solve this, however, you can always download an application like Towelroot from Uptodown.
adAway is an excellent tool for blocking ads, and although it isn't available via Google Play (or perhaps because of it), it has plenty of great features. Plus, its user interface is simple, convenient, and easy to set up.