AdAway has been around for as long as I can tremember. It was always one of the first apps I installed when I had a rooted device. However, when it comes to 'non-rooted' I  did mention multiple great options in the past. You have plenty of choices with  RethinkDNS, AdGuard, NetGuard and the like.

AdAway is simple, and on rooteds it doesn't take your VPN slot away. Using rooted device, the application updates your system hosts file that contains a list of mappings between host names and IP addresses. On non-rooted devices, AdAway uses the VPN slot just like any other firewall.

Y0u can update and add your own blocklists and domains on the list, getting redirects to the local IP 127.0.0.1, which does nothing. There are options to run a local web server to respond to blocked host names and to direct requests to the IP address of your choosing instead.

AdAway is available on F-Droid.

AdAway | F-Droid - Free and Open Source Android App Repository

F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.

Free and Open Source Android App Repository

It is fully open-source and simple to use. Unlike NetGuard, AdGuard, RethinkDNS and the like, you can't block apps or system apps from having access to the internet, which leaves you with an excellent ad blocker, but you can't really block access entirely to specific apps. On Root, AdAway does not use the VPN slot, which is way more powerful. If you go in the direction of rooting your Android device, AdAway with AFWall+ is the best solution out there.

AFWall+ | F-Droid - Free and Open Source Android App Repository

F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.

Free and Open Source Android App Repository

Please remember, rooting a device might be opening the best option when it comes to privacy, but it also opens a bigger attack surface and other security treats. This is one reason why I've gone non-rooted for a few years.

I have been contacted to write about Blockada as a potentially excellent firewall and ad blocker, however, I need to admit I've never liked it. RethinkDNS had an article which mentioned a few things which just doesn't sit well with me and there was another site with critical comments about Blockada.

Blokada anti-features: Paid features and trackers (!8536) · Merge requests · F-Droid / Data

Blokada upsells a paid VPN service right on the homescreen. Tagging the app as such, as it is an anti-feature as far as f-droid is concerned.

GitLab

As you might realize seeing the posts about DNS and firewalls and perhaps combinations of both worlds, Android really does give you some great choices.

Bear in mind with a firewall which takes the VPN slot you can't use a VPN at the same time, except when you go with a rooted device. AdGuard with AdGuardVPN has both options covered on a non-rooted device.

Stay safe!