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A set of very appealing phenomenological implications arise when baryon and lepton numbers are promoted to gauge theories. In the context of the simplest versions of local baryon or/and lepton number theories, anomaly cancellation predicts the existence of a dark matter candidate, whose stability is guaranteed by an accidental symmetry that appears after the spontaneous breaking of these symmetries. Furthermore, baryon (or/and lepton) number must be broken in three units, what guarantees the stability of the proton and allows the theory to live at the low scale in consistency with all experimental bounds. Last but not least, as we will see in this talk, baryon or/and lepton numbers must be violated below the multi-TeV scale in order to be in agreement with cosmology, what brings us the chance to explore the correlation between signals at our current (or near future) dark matter and collider experiments.