  We review in this paper the research status on testing the completeness of
Quantum mechanics in High Energy Physics, especially on the Bell Inequalities.
We briefly introduce the basic idea of Einstein, Podolsky, and Rosen paradox
and the results obtained in photon experiments. In the tests of Bell
inequalities in high energy physics, the early attempts of using spin
correlations in particle decays and later on the mixing of neutral mesons used
to form the quasi-spin entangled states are covered. The related experimental
results in K^0 and B^0 systems are presented and discussed. We introduce the
new scheme, which is based on the non-maximally entangled state and proposed to
implement in \phi factory, in testing the Local Hidden Variable Theory. And, we
also discuss the possibility in generalizing it to the tau charm factory.
