I have been on and off using Brave since around January of this year. Shortly after I began using it, I made a few pull requests to add minor features I really wanted to have, such as navigating back/forward with mouse buttons. The browser is effectively a Chromium wrapper, using Electron to launch a JS app as a desktop application. If you look into the codebase, you'll quickly find that it's actually even a React application, which makes it very approachable to hack on for anyone into that.
Brave's main claim to fame is that it blocks things like tracking scripts and pixels, and will either block ads or replace them with less obnoxious, safer ads from their own network. This has caused a bit of a stir now that the browser and startup behind it (lead by Brendan Eich) have gotten some notoriety. Some news websites are banding together to take down the project, saying that from their perspective, replacing their ads is no different than republishing their work for gains.
This is my latest return to the browser, after I saw that it now natively supports 1password, a password manager. 1Password has a killer feature of letting me press a hotkey to log in to a website. It takes away the most painful step of browsing, and I really missed it from Chrome. After returning to Brave, I was happy to see that some of my other complaints have already been addressed, such as http auth not being totally supported (you could still put it in your url, but now they have a popup box), and not having a context menu item for "Inspect Element".
Regardless of legal drama, it is worth trying the browser out if you are at all concerned with tracking or ads overstepping their bounds. I'm not a total fan of adblock, but I also don't like having so much unnecessary bloat downloaded from sites I visit. Since Brave never even requests non-primary resources, it loads websites lightning fast. I have, however, run into issues where it doesn't load actual important material, but the developers of the browser seem to be addressing this issue site-by-site. That may take a while, but hopefully we'll see better pairity with other browsers soon enough.
Also, don't bother with the mobile versions. They're just rebranding of existing instapaper-like applications. If you're on Android, I recommend Flynx instead.