  To seek high-$T_c$ pairing mechanism, many scientists have focused on the
mysterious spontaneous rotational symmetry breaking above Tc, such as nematic
order at $q=0$ and smectic order at $q\ne0$. Such exotic correlation-driven
symmetry breaking in metals has become a central issue in condensed matter
physics. We demonstrate the emergence of the nematic and smectic orders due to
orbital polarization ($n_{xz}\ne n_{yz}$) and the symmetry breaking in the
correlated intersite hopping (= bond order $\delta t_{i,j}$) in Fe-based and
cuprate superconductors. In addition, we discuss exotic spontaneous loop
current orders driven by the pure imaginary $\delta t_{i,j}$. These interesting
``unconventional density-waves'' originate from the quantum interference
between different spin fluctuations that is described by the vertex correction
(VC) in the field theory. In the next stage, we discuss electron-correlation
driven superconductivity due to the fluctuations of unconventional
density-waves. For this purpose, we suggest the beyond-Migdal-Eliashberg gap
equation by including the VCs into the equation. In Fe-based superconductors,
high-$T_c$ $s$-wave superconductivity can be mediated by nematic and smectic
fluctuations because the pairing interaction is magnified by the VCs. We also
discuss the multipolar fluctuation pairing mechanism in heavy fermion systems,
owing to the cooperation between the strong spin-orbit interaction and the
strong electron correlation. To summarize, we suggest that the quantum
interference mechanism described by the VCs is the key ingredients to explain
not only various unconventional density-waves, but also exotic superconducting
states in many strongly correlated metals. We finally discuss some interesting
future issues with respect to the quantum interference mechanism.
