@Treppenwitz @KitRedgrave I'd like to add one point: This only discusses the browser end of things.
Any app that has its own web connection can display ads independent of the browser. This is especially prevalent on mobile devices.
To block ads for such apps, you'd need a systemwide adblocker, which requires either rooting your device or using the built-in proxy system.
If you also use a firewall or proxy server app, your only choice is to root.
@Treppenwitz @KitRedgrave Also worth noting that Google has decided that systemwide adblockers violate their developer's agreement, so they are banned from the Play Store. Any you find there are not real & likely ripoffs of the open-source versions that could contain malware.
As such, we're forced to sideload them, preferably using an alternative app store like F-Droid. AdAway uses root, while DNS66 uses the proxy system. These are the most reliable adblockers for Android.