  The eigenvalues for the minors of real symmetric ($\beta=1$) and complex
Hermitian ($\beta=2$) Wigner matrices form the Wigner corner process, which is
a multilevel interlacing particle system. In this paper, we study the
microscopic scaling limit of the Wigner corner process both near the spectral
edge and in the bulk, and prove they are universal. We show: (i) Near the
spectral edge, the corner process exhibit a decoupling phenomenon, as first
observed in [24]. Individual extreme particles have Tracy-Widom$_{\beta}$
distribution; the spacings between the extremal particles on adjacent levels
converge to independent Gamma distributions in a much smaller scale. (ii) In
the bulk, the microscopic scaling limit of the Wigner corner process is given
by the bead process for general Sine$_\beta$ process, as constructed recently
in [34].
