What is CP?
In 1964, James Cronin, Val Fitch with co-workers provided clear evidence (which was first announced at the 12th ICHEP conference in Dubna) that CP symmetry could be broken, too, winning them the 1980 Nobel Prize. This discovery showed that weak interactions violate not only the charge-conjugation symmetry C between particles and antiparticles and the P or parity, but also their combination. The discovery shocked particle physics and opened the door to questions still at the core of particle physics and of cosmology today. The lack of an exact CP symmetry, but also the fact that it is so nearly a symmetry created a great puzzle.
Only a weaker version of the symmetry could be preserved by physical phenomena, which was CPT-symmetry. Besides C and P, there is a third operation, time reversal (T), which corresponds to reversal of motion. Invariance under time reversal implies that whenever a motion is allowed by the laws of physics, the reversed motion is also an allowed one. The combination of CPT is thought to constitute an exact symmetry of all types of fundamental interactions. Because of the CPT-symmetry, a violation of the CP-symmetry is equivalent to a violation of the T-symmetry. CP violation implied nonconservation of T, provided that the long-held CPT theorem was valid. In this theorem, regarded as one of the basic principles of quantum field theory, charge conjugation, parity, and time reversal are applied together.
The kind of CP violation discovered in 1964 was linked to the fact that neutral kaons can transform into their antiparticles (in which each quark is replaced with its antiquark) and vice versa, but such transformation does not occur with exactly the same probability in both directions; this is called indirect CP violation. Despite many searches, no other manifestation of CP violation was discovered until the '90s, when the NA31 experiment at CERN suggested evidence for CP violation in the decay process of the very same neutral kaons, so-called direct CP violation. The observation was somehow controversial, and final proof for it came in 1999 from the KTeV experiment at Fermilab and the NA48 experiment at CERN.
In 2001, a new generation of experiments, including the BaBar Experiment at the Stanford Linear Accelerator Center (SLAC) and the Belle Experiment at the High Energy Accelerator Research Organisation (KEK) in Japan, observed CP violation in a different sector of particle physics, namely in decays of the B mesons [1]. By now a large number of CP violation processes in B-meson decays have been discovered. Before these "B-factory" experiments, it was a logical possibility that all CP violation was confined to kaon physics. However, this raised the question of why it's not extended to the strong force, and furthermore, why this is not predicted in the unextended Standard Model, despite the model being undeniably accurate with "normal" phenomenon.
The CP violation is incorporated of the Standard model by including a complex phase in the CKM matrix describing quark mixing. In such scheme a necessary condition for the appearance of the complex phase, and thus for CP-violation, is the presence of at least three generations of quarks.
There is no experimentally known violation of the CP-symmetry in quantum chromodynamics; see below.

Strong CP problem

Main article: Baryogenesis