I will briefly motivate the use of discrete symmetries in flavored model building before presenting a model-independent, bottom-up procedure for finding finite groups that yield acceptable phenomenology. I will give results of one such scan in the lepton sector and describe how one might extend the search to the case of a flavour symmetry combined with a generalized CP symmetry, as well as extensions to the quark sector. Finally, I will discuss the current status of the discrete symmetry paradigm and mention how we might look for constraints on this physics from the UV.