CP violation -- the non-invariance of physical laws under the combined transformation of charge conjugation (C, swapping particle and antiparticle) and parity (P, mirror reflection) -- was discovered in 1964 in the neutral kaon system. In the Standard Model, CP violation arises from the complex phase in the CKM matrix. It is a necessary condition for generating the matter-antimatter asymmetry of the universe (one of the Sakharov conditions), though the amount of CP violation in the Standard Model appears insufficient to explain the observed asymmetry.
CP violation is one of the most profound features of the weak interaction and one of the deepest unsolved problems in physics. Discovered in 1964 in the decay K_L -> pi+ pi- (Cronin and Fitch, Nobel Prize 1980), it means that the laws of physics distinguish between matter and antimatter -- a universe made of antimatter would evolve differently from ours. In the Standard Model, CP violation is encoded in the single complex phase of the CKM matrix, predicted by Kobayashi and Maskawa in 1973 as a consequence of having three or more generations of quarks.
The neutral kaon system exhibits CP violation in two distinct ways. Indirect CP violation (parameterized by epsilon) arises from the slight CP impurity in the K_L mass eigenstate due to K-Kbar mixing. The mass eigenstates K_S and K_L are not exactly the CP eigenstates K_1 and K_2 but are rotated by an angle epsilon in the complex plane. Direct CP violation (parameterized by epsilon-prime) occurs when the decay amplitudes themselves violate CP. The ratio Re(epsilon'/epsilon) ~ 1.7 x 10^{-3} was measured after decades of effort by the NA48 and KTeV experiments, confirming that CP violation exists in the decay amplitude itself, not just in mixing.
The B meson system provides the most precise tests of the CKM mechanism of CP violation. The B_d and B_s mesons undergo rapid matter-antimatter oscillation, and the interference between mixing and decay produces time-dependent CP asymmetries that are directly related to angles of the unitarity triangle. The B factory experiments (BaBar, Belle) and LHCb have measured: sin(2*beta) from B -> J/psi K_S with 2% precision, the angle alpha from B -> pi pi and rho rho, and the angle gamma from B -> DK. All measurements are consistent with a single CKM phase, confirming the Standard Model picture to high accuracy.
Despite the success of the CKM description, the cosmological matter-antimatter asymmetry requires CP violation beyond the Standard Model. The observed baryon-to-photon ratio (~6 x 10^{-10}) is about 10 orders of magnitude larger than what CKM CP violation can produce. New sources of CP violation might exist in the lepton sector (leptogenesis via the neutrino mixing matrix), in extended Higgs sectors (additional scalar phases), or in supersymmetric models (new complex phases in squark and gaugino sectors). Searches for CP violation in the Higgs sector, in neutrino oscillations, and in electric dipole moments of fundamental particles are among the highest-priority experiments in particle physics.