  The strong CP problem can be solved if the laws of nature are invariant under
a space-time parity exchanging the Standard Model with its mirror copy. We
review and extend different realizations of this idea with the aim of
discussing Dark Matter, neutrino physics, leptogenesis and collider physics
within the same context. In the minimal realization of Ref. [1] the mirror
world contains a massless dark photon, which leads to a rather interesting
cosmology. Mirror electrons reproduce the dark matter abundance for masses
between 500-1000 GeV with traces of strongly interacting dark matter. This
scenario also predicts deviations from cold dark matter, sizable $\Delta N_{\rm
eff}$ and colored states in the TeV range that will be tested in a variety of
upcoming experiments. We also explore scenarios where the mirror photon is
massive and the mirror particles are charged under ordinary electro-magnetism
with very different phenomenology. We also show that, for the measured values
of the SM parameters, the Higgs effective potential can give rise to a second
minimum at large field value as required to break spontaneously the parity
symmetry.
