Given the success of the standard Cold Dark Matter (CDM) structure formation model in describing the large-scale structure of the Universe, the search to identity the dark matter particle(s) has focused on candidates that behave as CDM. Despite great efforts, these searches remain fruitless. Surprisingly, current observations allow for significant departures from the CDM hypothesis, where non-gravitational dark matter interactions play a significant role in the formation and evolution of galaxies. These deviations are possible in a regime where the ordinary (baryonic) physics of galaxies remain uncertain and thus to a large degree, baryonic and new dark matter physics are currently degenerate. In this talk I will argue that this breaking this degeneracy is a key endeavour in the field of galaxy formation and a promising avenue to make progress in our quest to identify the particle properties of dark matter.