  We study the Nambu-'t Hooft picture for color confinement in terms of the
abelianization of QCD and monopole condensation in the maximally abelian (MA)
gauge. In the MA gauge in the Euclidean metric, the off-diagonal gluon
amplitude is strongly suppressed, and then the off-diagonal gluon phase shows
strong randomness, which leads to rapid reduction of the off-diagonal gluon
correlation. In SU(2) and SU(3) lattice QCD in the MA gauge with the abelian
Landau gauge, the Euclidean gluon propagator indicates a large effective mass
of the off-diagonal gluon as $M_{\rm off} \simeq 1 {\rm GeV}$ in the
intermediate distance as $0.2{\rm fm} \le r \le 0.8{\rm fm}$. Due to the
infrared inactiveness of off-diagonal gluons, infrared QCD is well abelianized
like nonabelian Higgs theories in the MA gauge. We investigate the
inter-monopole potential and the dual gluon field $B_\mu$ in the MA gauge, and
find longitudinal magnetic screening with $m_B \simeq$ 0.5 GeV in the infrared
region, which indicates the dual Higgs mechanism by monopole condensation. We
define the ``gluonic Higgs scalar field'' providing the MA projection, and find
the correspondence between its hedgehog singularity and the monopole location
in lattice QCD.
