My most favorite pot scrubbing tool is a scotchbrite pad, especially the one without any sponge and not the one that is meant for teflon. No, the powerful one that takes off the most minute stains in stainless steel.
Unfortunately, as do all things in this world, the pads wear out pretty quickly. Others use things like Bar Keepers Friend and Ajax etc, all of which carry warnings not to breathe in. No thanks. And baking soda just doesn't do much in this case.
But then there's something I learned in India. People cleanse their stainless with sand. Luckily, we have areas of fine sand where the soil is washed away by continuous rains. Couple that with the homemade sponges mentioned earlier and you will learn how Indians keep their pots so shiny. Or use any terry cloth or sponge, etc. that can be used to rub on the sand.
The example below is not the best. This pot had not been scrubbed in a very long time so the stain required a lot of elbow grease but its now looking a lot better. Next time I'll get the wok in here after a cooking session that even metal steel scrubbers cannot remove but the sand and luffa does with ease!
Ok here’s the wok it was a mess, but I missed hitting a photo of that. Anyway, first the grease was removed with a regular long handled brush to keep hands out of the dish soap.
Next, the stainless steel metal scrubber was used.
And the remaining stain as seen in the photo could not be removed with the metal scrubber was easily removed with a loofah and a little sand outside in my designated pot scrubbing area.
Success! Best of all it was done with natural supplies from Krishna.
UPDATE : the luffa is such a gentle cleanser along with fine sand; we discovered it can polish copper and silver, too.
PS Some people are repulsed by this idea for some reason I personally don't understand, but I've seen regular soil ( that isn't contaminated, of course) is also used if sand is not available. And it works, too!