  A review of the coupled cluster method (CCM) applied to lattice quantum spin
systems is presented here. The CCM formalism is explained and an application to
the spin-half {\it XXZ} model on the square lattice is presented. Low orders of
approximation are carried out analytically and a high-order CCM formulation is
presented. Results for the SUB2 approximation are carried out numerically for
SUB2-$m$ and analytically for SUB2. It is found that SUB2-$m$ results converge
rapidly to the full SUB2 solution, including new results for the SUB2-$m$
limiting points compared to the SUB2 critical point. Results for the
ground-state energy and the sublattice magnetisation are presented. A study of
the excitation spectrum of this model at the SUB2 critical point is given.
Indeed, the shape of the excitation spectrum at the SUB2 critical point is
identical to that predicted by spin-wave theory for the isotropic model, albeit
with a multiplicative factor of 1.1672. This result compares very well to
results of cumulant series expansions and Monte Carlo simulation that again
predict a similar shape for the excitation spectrum, but with multiplicative
factors of 1.18 and 1.21$\pm$0.03, respectively. Results for the isotropic
Heisenberg model on the square lattice for the spin-one antiferromagnet and the
spin-one/spin-half ferrimagnet are also given.
