Vanilla is an open source and free forum platform if you host it on your own server. They offer a cloud hosting as a paid subscription.
The platform looks modern, but does not have included many common options that other free or paid platforms have.
The have an active add-on marketplace where you can find different plugins to extend the functionality.
The platform offers the essential options to manage the forum.
Does not include by default private messaging and friend list. many features are available via addons.
The admin interface looks well organized and with essential features. many addons are available to install from the developer's website.
They have an active forum where you can ask questions and receive help.
Vanilla is not so popular as other platforms, but comes with a new look and feel that you could like. You can use it for free and you can subscribe on their cloud plans if you like it.