CP symmetry

A natural thought upon noticing the parity-violating interactions (Co-60 beta decay, neutrino helicity, and the theta-tau puzzle, for instance) is that if instead of applying only a parity transformation, we instead apply a parity transformation followed by a charge conjugation (switch particles for antiparticles), we might get the same laws of nature. So for instance reflecting a neutrino in a mirror results in a neutrino with the opposite helicity, which we never see in nature. But if we also change it to an antineutrino, then the helicity is as needed for an antineutrino. Similarly, if we both look in a mirror and use anti-cobalt-60, then the positrons (anti-electrons) are emitted in the same direction as the nuclear spin, so it seems that CP symmetry should hold.
Unlike P-symmetry, which is maximally violated in weak interactions, CP symmetry is mostly true (and appears to be exact in strong and electromagnetic interactions), and it took a while for physicists to find an interaction in which CP was violated. The first (indirect) evidence for CP violation came from the neutral kaon system, which I'm sure I'll write extensively about in the future. Since then, neutral kaons have yielded direct CP violation, as have B and D mesons, so it's a well-established fact that CP is not an exact internal symmetry.
This has a few interesting implications. For one thing, CP violation is able to favor matter over antimatter, which can at least partially explain why the universe we live in appears to be made entirely of matter.* Basically in the Big Bang, since the forces were primarily electromagnetic and strong forces, CP should have been an exact symmetry, which means that for a while, at least, the universe had exactly as much matter as antimatter. The question then becomes what allowed the universe to evolve into predominantly matter, and CP violation says that through weak interactions, matter and antimatter can be distinguished and preferentially generated.
CP violation also means that we can finally absolutely define the positive charge, whereas previously we simply had to stick with a convention based on rubbing glass and silk together. We can say that positive is the charge of the lepton preferentially emitted in the decay of the neutral K meson (again, I'll explain more about these fascinating creatures in the nearish future).
Another interesting implication is that quantum field theory predicts that the combined CPT transformation should be an exact symmetry in all interactions. Remember that T is a transformation that reverses the direction of time. The derivation of that idea is way beyond me, but it's apparently based only on the basics; things like special relativity and the idea that only local properties can affect an interaction. And since CP is violated, if the CPT theorem holds, then T must be violated as well. T violation is a lot harder to detect than C, P, or CP violation, because we're pretty much stuck in a universe moving forwards in time, but physicists are diligently looking for things like a non-zero electric dipole moment of the neutron as we speak, which would imply T violation and allow a confirmation of the CPT theorem.

*If the universe had portions consisting of matter and portions of antimatter, we would expect that the interface would have an abundance of annihilation, which would appear as a bright layer without necessarily many stars around.