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The strong CP problem can be solved if the laws of nature are invariant undera space-time parity exchanging the Standard Model with its mirror copy. Wereview and extend different realizations of this idea with the aim ofdiscussing Dark Matter, neutrino physics, leptogenesis and collider physicswithin the same context. In the minimal realization of Ref. [1] the mirrorworld contains a massless dark photon, which leads to a rather interestingcosmology. Mirror electrons reproduce the dark matter abundance for massesbetween 500-1000 GeV with traces of strongly interacting dark matter. Thisscenario also predicts deviations from cold dark matter, sizable $\Delta N_{\rmeff}$ and colored states in the TeV range that will be tested in a variety ofupcoming experiments. We also explore scenarios where the mirror photon ismassive and the mirror particles are charged under ordinary electro-magnetismwith very different phenomenology. We also show that, for the measured valuesof the SM parameters, the Higgs effective potential can give rise to a secondminimum at large field value as required to break spontaneously the paritysymmetry.

Neutrinos, Dark Matter and Higgs Vacua in Parity Solutions of the strong CP problem