For the big stuck on pieces, you use a stainless steel chainmail scrubber. For cast iron pans you can scrub as hard as you can with that and you aren't hurting the pan. Try doing that on your aluminum, Teflon non-stick pan, or your nicely polished stainless steel pan and let me know how that goes (don't do this). For cleaning off oils and grease off cast iron, regular liquid dish soap (like Dawn) works great and is totally okay to use for cleaning cast iron.

For your cast iron, don't use lye based cleaners and don't put your cast iron in the dishwasher.

I got a fridge magnet like this a while ago for a friend:

They retain and distribute heat well. Also I can move it directly from my stove to my oven or vice versa

I have one that I only use to make cornbread. Cornbread doesn't make it dirty and cast iron is the only thing that will give you a proper crust on the cornbread.

The truly enlightened use carbon steel pans.