  In this report, we describe a recent development in a Fermi liquid theory for
the Kondo effect in quantum dots under a finite bias voltage $V$. Applying the
microscopic theory of Yamada and Yosida to a nonequilibrium steady state, we
derive the Ward identities for the Keldysh Green's function, and determine the
low-energy behavior of the differential conductance $dI/dV$ exactly up to terms
of order $(eV)^2$ for the symmetric Anderson model. These results are deduced
from the fact that the Green's function at the impurity site is a functional of
a nonequilibrium distribution $f_{\text{eff}}(\omega)$, which at $eV=0$
coincides with the Fermi function. Furthermore, we provide an alternative
description of the low-energy properties using a renormalized perturbation
theory (RPT). In the nonequilibrium state the unperturbed part of the RPT is
determined by the renormalized free quasiparticles, the distribution function
of which is given by $f_{\text{eff}}(\omega)$. The residual interaction between
the quasiparticles $\widetilde{U}$, which is defined by the full vertex part at
zero frequencies, is taken into account by an expansion in the power series of
$\widetilde{U}$. We also discuss the application of the RPT to a high-bias
region beyond the Fermi-liquid regime.
