What are they?

WASD to move, arrow keys to shoot in up/down/left/right, 1 to place/detonate a bomb, 2 to use blades. The keyboard player can also use the mouse to fire the turret with the left button, the blades with the right button, and bombs with the middle button. 

This keyboard setup might not work that well with non-QWERTY layouts, in which case you can edit the config file, located in C:\Users\<user>\AppData\Roaming\spacebeef on Windows, and (I think) ~/.config/spacebeef on Linux.

I also just found some input-related bugs while checking something so I'm uploading a new build now to address those.

The format of that config file is kind of messy, may address that at some point.

Any chance of having the controls configurable by in-game settings?

Yeah, can't give an exact ETA on that but I'll put it on the feature list.