@Susan G a friend turned me on to cameo cleanser. It works on the bottom of pots and pans as well as well as the inside when you char the food. I used to be able to get this in any grocery store but now I can only get it in the home section of the hardware store.
I do most of my cooking in cast iron...the inside and the outside are all pretty much the same...well seasoned and satiny black.
for the one or two sauce pans that are hard anodized aluminum I scrub them with my green kitchen scrubie.
Barkeeper's Friend. Amazing with many uses. Easily found at Walmart, hardware stores, etc.
I also use bar keeps friend, however if it really needs an overhaul, try oven cleaner, we had to do that to our old stainless pan bottoms once. after that I keep a keen eye on the bottoms! But Bar keeps friend is really good, paper towel, wet it, dab into the barkeeps and scrub away. It really Is amazing how easy it is for how bad the bottoms can get! I love seeing the black/brown come off. Some things just make your day!