Falkon is a Qt5 web browser developed by KDE. Previously an independent project named QupZilla, it joined KDE in 2017 and quickly saw work done to rebrand and bring it up to scratch with modern standards. It uses Qt WebEngine as a backend, giving it the same web standard compliance and general performance as Google Chrome, though it's often reported to be more lightweight than Chrome/Chromium.
Compared to other mainstream browsers, Falkon sees fantastic integration with KDE, thanks largely to being one of the few browsers to use Qt 5. It can use native scrollbars, store passwords in KWallet, integrate with KDE PIM, print with the native Qt dialog, and it always uses a native look-and-feel to align with your system and icon theme. It also is much smarter than Firefox about opening downloaded files in your system's default application for that filetype.
An AdBlock is included and enabled by default, and other extensions are built-in and available such as GreaseMonkey, a reverse image search, mouse gestures, tree-style tabs, and an autoscroll. It also features a lot of general customizability and configuration, as is typical for KDE apps.
Starting in Falkon 3.1, Falkon has support for custom extensions written in Python or QML, along with tighter integration with the KDE Frameworks, allowing you to make use of its sharing features. This, in effect, also gives Falkon a level of integration with KDE Connect.
Privacy and Security
It must be stressed though that most of these require manual intervention to make the most of. Most importantly, XSS auditing is disabled by default, and the password manager stores a plaintext database. It's strongly recommended to look through the settings prior to use in an insecure environment, and make sure they're up to scratch with how secure you want your browser to be. The built-in AdBlock also has a preset to enable EasyPrivacy when you try to add a subscription, which you may enjoy for safer browsing.
Falkon supports both QML and Python extensions in versions 3.1 and newer. While it has many built-in, third-party extensions can be found on the official Falkon Store and installed manually, though it's always a good idea to read the source before running untrusted third-party code in your browser.
Falkon 3.1 will scan for extensions in the ~/.config/falkon/plugins/ and /usr/lib/qt/plugins/falkon/python/ directories, used for user-specific or system-wide installs respectively. Downloaded archives from the Falkon Store will generally contain a folder you can place in either of these.
Falkon doesn't (currently!) support WebExtensions, meaning that any extensions designed for Chrome or Firefox are incompatible, unless rewritten and ported to Falkon's extension API. Support for WebExtensions would need to be first implemented in Qt WebEngine, the progress of which is tracked in the Qt Bug Tracker: https://bugreports.qt.io/browse/QTBUG-61676
IRC Channel: #falkon at chat.freenode.net