Q:

How do I turn off these bounding boxes?

When editing my model, it looks like this:

when I press P to go into 'game-mode' (or however it is called)
it looks like this.

This question is NOT about the Texture space bounding box (dashed orange or black, depending on selection state) around the selected object. This I can turn off in the properties area, in the objects tab, in the Display panel, by ticking off the Texture Space.
It is also not about the bounding boxes you get by selecting a different viewport shading. As you can tell by the right most object, the red bounding boxes are bigger than the objects Texture space, ... or viewport bounding box (I checked).
What are the red boxes surrounding my objects?
Why are some meshes green while others are not shown at all?

A:

Uncheck "Show Physics Visualization."

