  The purpose of this paper is two-fold: we systematically introduce the notion
of Cheeger deformations on fiber bundles with compact structure groups, and
recover in a very simple and unified fashion several results that either
already appear in the literature or are known by experts, though are not
explicitly written elsewhere. We re-prove: Schwachh\"ofer--Tuschmann Theorem on
bi-quotients, many results due to Fukaya and Yamaguchi, as well as, naturally
extend the work of Searle--Sol\'orzano--Wilhelm on regularization properties of
Cheeger deformations, among others. In this sense, this paper should be
understood as a survey intended to demonstrate the power of Cheeger
deformations. Even though some of the results here appearing may not be known
as stated in the presented form, they were already expected, being our
contribution to the standardization and spread of the technique via a unique
language.
