  A comprehensive theoretical and experimental study is presented of the
magnetic susceptibility versus temperature \chi(T) of spin S = 1/2 two- and
three-leg Heisenberg ladders and ladder oxide compounds. Extensive quantum
Monte Carlo simulations of \chi(T) were carried out for both isolated and
coupled two-leg ladders with spatially anisotropic intraladder exchange.
Accurate fits to these and related literature QMC data were obtained. We have
also calculated the one- and two-magnon dispersion relations and the dynamical
spin structure factor for anisotropic isolated 2 x 12 ladders. The exchange
constants in the two-leg ladder compound SrCu2O3 are estimated from LDA+U
calculations. We report the detailed crystal structure of SrCu2O3 and of the
three-leg ladder compound Sr2Cu3O5. New experimental \chi(T) data are reported
for the two-leg ladder cuprates SrCu2O3 and LaCuO_{2.5}, and for the
(nominally) two-leg ladder vanadates CaV2O5 and MgV2O5. The new and literature
\chi(T) data for these compounds and for Sr2Cu3O5 are modeled using our QMC
\chi(T) simulation fits, and the exchange coupling constants between the
spins-1/2 are thereby estimated for each material. The surpisingly strong
spatial anisotropy of the bilinear intraladder exchange constants in the
cuprate compounds is discussed together with the results of other experiments
sensitive to this anisotropy. Recent theoretical predictions are discussed
including those which indicate that a four-spin cyclic exchange interaction
within a Cu4 plaquette is important to determining the magnetic properties and
which can significantly influence the exchange interactions estimated from
\chi(T) data assuming the presence of only bilinear exchange.
