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The last 15 years have witnessed important progresses in our understanding ofthe mechanism of superconductivity in the high-$T_{c}$ cuprates. There is nowstrong evidence that the strange metal behavior is induced by the quantumcritical fluctuation at the pseudogap end point, where the Fermi surfacechanges its topology from hole-like to electron-like. However, experiments showthat the quantum critical behavior in the high-$T_{c}$ cuprates isqualitatively different from that observed in the heavy Fermion systems and theiron-based superconductors, in both of which the quantum critical behavior canbe attributed to the quantum phase transition toward a symmetry breaking phase.The fact that the pseudogap exists as a spectral gap without a correspondingsymmetry breaking order, together with the fact that the strange metal behavioroccurs as a quantum critical behavior without a corresponding symmetry breakingphase transition, exposes the central difficulty of the field: the lack of auniversal low energy effective theory description of the high-$T_{c}$phenomenology beyond the Landau paradigm. Recent experiments imply that thedualism between the local moment and the itinerant quasiparticle character ofthe electron in the high-$T_{c}$ cuprates may serve as an organizing principleto go beyond the Landau paradigm and may hold the key to the mystery of thepseudogap phenomena and the strange metal behavior.

A short review of the recent progresses in the study of the cuprate superconductivity