  To what extent are all astrophysical, dark, compact objects both black holes
(BHs) and described by the Kerr geometry? We embark on the exercise of defying
the universality of this remarkable idea, often called the "Kerr hypothesis".
After establishing its rationale and timeliness, we define a minimal set of
reasonability criteria for alternative models of dark compact objects. Then, as
proof of principle, we discuss concrete, dynamically robust non-Kerr BHs and
horizonless imitators, that 1) pass the basic theoretical, and in particular
dynamical, tests, 2) match (some of the) state of the art astrophysical
observables and 3) only emerge at some (macroscopic) scales. These examples
illustrate how the universality (at all macroscopic scales) of the Kerr
hypothesis can be challenged.
