  We present here three analyses of semileptonic $D$-meson decays based on the
2.92 fb$^{-1}$ of data collected by the BESIII experiment in 2010 and 2011 at
the $\psi$(3770) peak. For the decay $D^{+}\to K^{-}\pi^{+}e^{+}\nu_{e}$, its
branching fraction is measured over the whole $m_{K\pi}$ region and in the
$\overline{K}^{*}(892)^{0}$ window, respectively. A partial wave analysis (PWA)
is performed, indicating an \emph{S}-wave contribution of about 6\%. The
\emph{S}-wave phase and the form factors are measured by the PWA and in a
model-independent way. For the decay $D^{+}\to \omega e^{+}\nu_{e}$, an
improved measurement of the branching fraction is performed and the form
factors are determined for the first time. $D^{+}\to \phi e^{+}\nu_{e}$ is
searched and an improved upper limit at 90\% confidence level is set. For the
decay $D^{+}\to K_{L} e^{+}\nu_{e}$, its branching fraction is measured for the
first time and the $CP$ asymmetry is presented. The product of the hadronic
form factor and the CKM matrix element, $f_{+}^{K}(0)|V_{cs}|$, is also
determined in this decay.
