I am new to Inkscape, but have managed to build a shape I like for a (vector) logo. It's some rectangles and elipses.
What I would like to do now is distress it. I want it to look distressed, as though it's been damaged. I want pieces missing from it (so I can see through the shape).

I had thought there would be a way to use a brush to subtract from the shape, but maybe that's not the way to do it. I guess I need help in thinking about the strategy to make it look like a piece of metal that's had chunks scrapped away from it. (I can worry about surface texture later).

How would Inkscape look at my shape and subtract from it?

Even pretty advanced users find it best practice to start with a reference photo when trying to recreate textures in vector format. Also, if you show us what you are shooting for better advice than mine will surely be forthcoming

There´are a few filters onboard waiting for you to tweak:

...but the filter UI is not made for me - unfortunately.

Cheers

There's also the 'tweak' tool that can roughen a path.

In addition to that, there's a roughen extension and a roughen Live Path effect.

And you can vectorize images of dirt, and subtract that from the shape.

Dirt generators are available in the extensions gallery at inkscape.org: https://inkscape.org/gallery/=extension/