  One distinguishes between "true" CP violating triple product (TP) asymmetries
which require no strong phases and "fake" asymmetries which are due to strong
phases but require no CP violation. So far a single true TP asymmetry has been
measured in $K_L\to \pi^+\pi^- e^+e^-$. A general discussion is presented for
T-odd TP asymmetries in four-body decays. It is shown that TP asymmetries
vanish for two identical and kinematically indistinguishable particles in the
final state. Two examples are $D^0\to K^-\pi^+\pi^-\pi^+$ and $D^+\to
K^-\pi^+\pi^+\pi^0$. A non-zero TP asymmetry can be expected when non-trivial
kinematic correlations exist, as in the decay $K_L \to e^+ e^- e^+ e^-$. Triple
product asymmetries measured in charmed particle decays indicate an interesting
pattern of final-state interactions. We reiterate a discussion of TP
asymmetries in $B$ meson decays to two vector mesons each decaying to a
pseudoscalar pair, extending results to decays where one vector meson decays
into a lepton pair. We derive expressions for time-dependent TP asymmetries for
neutral B decays to flavorless states in terms of the neutral $B$ mass
difference $\Delta m$ and the width-difference $\Delta\Gamma$. Time-integrated
true CP violating asymmetries, measurable for untagged $B_s$ decays, are shown
to be suppressed by neither $\Gamma_s/\Delta m_s$ nor $\Delta\Gamma_s/\Gamma_s$
if transversity amplitudes for CP-even and CP-odd states involve different weak
phases. In contrast, fake asymmetries require flavor tagging and are suppressed
by the former ratio when time-integrated. We apply our results to $B\to
K^*\phi$ and $B_s\to\phi\phi$ data and suggest an application for $B_s\to
J/\psi\phi$.
