  In this communication we discuss few topics related with modern experimental
data on the physics of light pseudoscalar mesons. It includes the contribution
of the pseudoscalar mesons to the muon anomalous magnetic moment (AMM), $g-2$,
the rare decays of light pseudoscalar mesons to lepton pair, the transition
form factors of pseudoscalar mesons at large momentum transfer, the pion
transversity form factor.
  Measuring the muon anomalous magnetic moment $g-2$ and the rare decays of
light pseudoscalar mesons into lepton pair $P\rightarrow l^{+}l^{-} $ serve as
important test of the standard model. To reduce the theoretical uncertainty in
the standard model predictions the data on the transition form factors of light
pseudoscalar mesons play significant role. Recently new data on behavior of
these form factors at large momentum transfer was supplied by the BABAR
collaboration. Within the nonlocal chiral quark model it shown how to describe
these data and how the meson distribution amplitude evolves as a function of
the dynamical quark masses and meson masses.
