Feeling abandoned by Adobe? Check out the video editing suites for penguins
Options for those lacking a Linux render farm
Cinelerra/Lumiera and Blender
Both Cinelerra and Blender are very complex, full featured editors, far too complex to go into any detail here. Suffice to say that Cinelerra is the closest Linux comes to an open source Avid/Final Cut Pro. It's correspondingly complex and, sadly, wrapped in an interface I'm pretty sure not even its mother could love.
A few years ago it was forked in an effort to, among other things, give it a face lift, but nothing seems to have come of that effort (dubbed Lumiera). Ugly as it maybe, Cinelerra is the most capable video editor of the bunch. If you want pro-level features, Cinelerra has most of them.
Blender is probably best known as an animation and rendering tool, particularly for 3D modeling, but it actually has a very nice and capable timeline editor in it as well. In fact, if you're coming from something like Premiere or Final Cut Pro, Blender may be the most familiar of the bunch and among the most capable.
There's clearly no shortage of Linux video editors. There's also half a dozen more out there that I haven't had time to test. The variety is nice, but it also complicated the decision – which one is right for you?
For quick video edits to a single clip, Avidemux fits the bill.
If you've got a few clips you'd like to combine, maybe add a audio track to and perhaps apply a filter before uploading to YouTube then Pitivi is probably your best bet, though OpenShot might be worth testing.
If you've got 4K video to edit and want to apply color correction and effects you'll need correspondingly more sophisticated tools. I prefer Kdenlive and have yet to find something I couldn't do with it, though Shotcut appears equally capable if you take the time to figure out its interface.
And of course if you do run into some limitations with the lighter weight options there's always Blender and Cinelerra. ®