  The last 15 years have witnessed important progresses in our understanding of
the mechanism of superconductivity in the high-$T_{c}$ cuprates. There is now
strong evidence that the strange metal behavior is induced by the quantum
critical fluctuation at the pseudogap end point, where the Fermi surface
changes its topology from hole-like to electron-like. However, experiments show
that the quantum critical behavior in the high-$T_{c}$ cuprates is
qualitatively different from that observed in the heavy Fermion systems and the
iron-based superconductors, in both of which the quantum critical behavior can
be attributed to the quantum phase transition toward a symmetry breaking phase.
The fact that the pseudogap exists as a spectral gap without a corresponding
symmetry breaking order, together with the fact that the strange metal behavior
occurs as a quantum critical behavior without a corresponding symmetry breaking
phase transition, exposes the central difficulty of the field: the lack of a
universal low energy effective theory description of the high-$T_{c}$
phenomenology beyond the Landau paradigm. Recent experiments imply that the
dualism between the local moment and the itinerant quasiparticle character of
the electron in the high-$T_{c}$ cuprates may serve as an organizing principle
to go beyond the Landau paradigm and may hold the key to the mystery of the
pseudogap phenomena and the strange metal behavior.
