  Recent developments of the theoretical investigations on the one-dimensional
Kondo lattice model by using the density matrix renormalization group (DMRG)
method are discussed in this review. Short summaries are given for the
zero-temperature DMRG, the finite-temperature DMRG, and also its application to
dynamic quantities. Away from half-filling, the paramagnetic metallic state is
shown to be a Tomonaga-Luttinger liquid with the large Fermi surface. For the
large Fermi surface its size is determined by the sum of the densities of the
conduction electrons and the localized spins. The correlation exponent K_rho of
this metallic phase is smaller than 1/2. At half-filling the ground state is
insulating. Excitation gaps are different depending on channels, the spin gap,
the charge gap and the quasiparticle gap. Temperature dependence of the spin
and charge susceptibilities and specific heat are discussed. Particularly
interesting is the temperature dependence of various excitation spectra, which
show unusual properties of the Kondo insulators.
