  The bulk properties and impurity effect in the one-dimensional S=1/2
Heisenberg model with dimerization and next-nearest-neighbor exchange are
studied by the density matrix renormalization group (DMRG) and exact
diagonalization methods. This model widely covers the S=1 Heisenberg model,
two-leg ladders, bond-alternating chains and the S=1/2 Heisenberg model. Almost
the whole parameter space belongs to the Haldane phase. In the non-dimerizing
limit a transition to a kind of spin liquid takes place, characterized by the
delocalized spin polarization. This transition causes the distinct impurity
effects between a spin-Peierls compound CuGeO_{3} and the Haldane systems.
Experimental aspects of a bond-alternating compound CuNb_{2}O_{6} are also
discussed. Furthermore, the incommensurate correlation arising in this model is
extensively studied, and a phase diagram is constructed.
