While singularities are inevitable in the classical theory of general relativity, it is commonly believed that they will not be present when quantum gravity effects are taken into account in a consistent framework. In particular, the structure of black holes should be modified in frameworks beyond general relativity that aim at regularizing singularities. Being agnostic on the nature of such theory, in this paper we classify the possible alternatives to classical black holes and provide a minimal set of phenomenological parameters that describe their characteristic features. The introduction of these parameters allows us to study, in a largely model-independent manner and taking into account all the relevant physics, the phenomenology associated with these quantummodified black holes. We perform an extensive analysis of different observational channels and obtain the most accurate characterization of the viable constraints that can be placed using current data. Aside from facilitating a critical revision of previous work, this analysis also allows us to highlight how different channels are capable of probing certain features but are oblivious to others, and pinpoint the theoretical aspects that should be addressed in order to strengthen these tests.