How and when is it allowed to treat najasah on items -without water-?

As we have many questions about the topic of najasah and doubts on whether it is cleaned or treated well. Like: https://islam.stackexchange.com/questions/433/how-to-properly-clean-carpet-from-najasah https://islam.stackexchange.com/questions/42575/ritual-impurity-in-pants https://islam.stackexchange.com/questions/49621/do-i-have-to-wash-the-undergarment https://islam.stackexchange.com/questions/62384/i-dont-remember-were-the-impurity-is https://islam.stackexchange.com/questions/36864/will-my-pure-clothes-become-impure-by-washing-them-in-a-washing-machine-with-imp https://islam.stackexchange.com/questions/2699/does-the-three-times-count-still-apply-if-we-use-detergent I'd like to ask a more general question on how to treat najasah on items in order to clean it (make it tahir again). As the question is general I expect an answer for all cases that scholars have discussed. Usually najasah is treated with water, and this is the major and primary solution to regain taharah. But there are other options, I'd like to know these options for cleaning najasah without water and when they apply? Please quote the scholarly view you are referring to in your answer, answers citing differences of opinion would be great. I'd also regard this question as a kind of compendium to my former question: https://islam.stackexchange.com/questions/46819/what-items-are-considered-najis-in-fiqh