You need a strong degreaser. I was looking at mine the other day and thinking it looks gross.
After cleaning so, so many very greasy college apartments, I learned that undiluted Pine-Sol is amazing on that stuff. I would take the knobs off the stove and soak them in it, and years of build-up would come off really easily with a toothbrush. You can apply it to the vents with the toothbrush and it ought not get too messy. Just get it wet with it. Then wipe it off with a rag.
I haven't tried it yet, but that's what I would/will try first.
Here's something else I learned that's related. You know the filters under the microwave (or under the vent hood) that get all coated with grease? If you put it in a clear plastic bag (like a Zip-loc, if it'll fit. Mine didn't, so I found something else) and pour in ammonia, then seal it and set it out in the sun, it loosens all the grease. Then you take the garden hose to it and it all comes off, shiny as new. I did it to my 1971 vent hood. It had been a rental, so I doubt anyone had ever cleaned it---ever! It was really really bad. It came completely clean.