I tried using baking soda to clean a really grungy oven from a rental unit. Worked great.
No, I don't mean I used the baking soda as an abrasive. I put a layer of baking soda on all the grunge, misted it heavily with water, and left it overnight.
In the morning, I wiped out the baking soda, and the vast majority of the grunge came right out with it. The spots that dried prematurely didn't do as well. I understand this works by saponifying (turning into soap) the oils in the grunge. Freaking amazing. No scrubbing. No chemicals that will eat your flesh rapidly, although I am now be careful not to expose myself (like most self-mobile biological things on this planet, I've got oil-based components) to baking soda for long periods of time, the stuff is a lot more potent (in a gradual way) than I thought.