I think for cleaning cookware, whatever material it is, you should first try with an abrasive. It can clean light to medium spots on the pans and pots.
But when the cookware is used very frequently and oil is used in it, it is likely to have layers of grease and lime build up on it. In this situation, the regular cleaners do not work very well so you can opt for a solvent to clean the heavy grease accumulated on the cookware.
A solvent can have either baking soda or vinegar in it as they help to dissolve the deposits of grease and limescale.