  Quantum spin-lattice systems in low dimensions exhibit a variety of
interesting zero-temperature phases, some of which show non-classical (i.e.,
non-magnetic) long-range orders, such as dimer or trimer valence-bond order.
These symmetry-breaking systems with localized valence bonds are referred to as
valence-bond lattices (VBL) in this article. A review of our systematic
microscopic formalism based on a proper set of composite operators for the
ground and excited states of the VBL systems is given. The one-dimensional (1D)
spin-$1\over2$ frustrated model is investigated in detail. Several possible VBL
systems on the 1D spin-1 chains, the 2D square and {\it kagom\'e} lattices are
also discussed. That our microscopic theory guarantees the rotational symmetry
of the VBL systems is emphasized.
