  We discuss the novel superconducting characteristics and unusual normal-state
properties of iron (Fe)-based pnictide superconductors REFeAsO$_{1-y}$
(RE=La,Pr,Nd) and Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$($T_{c}=$ 38 K) by means of
$^{57}$Fe-NMR and $^{75}$As-NQR/NMR. In the superconducting state of
LaFeAsO$_{0.7}$ ($T_{c}=$ 28 K), the spin component of the $^{57}$Fe-Knight
shift decreases to almost zero at low temperatures, which provide firm evidence
of the superconducting state formed by spin-singlet Cooper pairing. The nuclear
spin-lattice relaxation rates $(1/T_{1})$ in LaFeAsO$_{0.7}$ and
Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ exhibit a $T^{3}$-like dependence without a
coherence peak just below $T_{c}$, indicating that an unconventional
superconducting state is commonly realized in these Fe-based pnictide
compounds. All these events below $T_c$ are consistently argued in terms of an
extended s$_{\pm}$-wave pairing with a sign reversal of the order parameter
among Fermi surfaces. In the normal state, $1/T_1T$ decreases remarkably upon
cooling for both the Fe and As sites of LaFeAsO$_{0.7}$. In contrast, it
gradually increases upon cooling in Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$. Despite
the similarity between the superconducting properties of these compounds, a
crucial difference was observed in their normal-state properties depending on
whether electrons or holes are doped into the FeAs layers. These results may
provide some hint to address a possible mechanism of Fe-based pnictide
superconductors.
