  Hard X-ray surveys have uncovered a large population of heavily obscured AGN.
They also reveal a population of quasars with moderate obscuration at both
visible and X-ray wavelengths. We use Chandra selected samples of quasars from
the ELAIS Deep X-ray Survey (EDXS) and CDF-N to investigate the obscuration
towards the nuclei of moderately obscured AGN. We find an inverse correlation
between the optical to X-ray flux ratio and the X-ray hardness ratio which can
be interpreted as due to obscuration at visible and X-ray wavelengths. We
present detailed optical and near-infrared data for a sample of optically-faint
(R>23) quasars from the EDXS. These are used to constrain the amount of
rest-frame UV/optical reddening towards these quasars. It is found that
optically-faint quasars are mostly faint due to obscuration, not because they
are intrinsically weak. After correcting for reddening, the optical magnitudes
of most of these quasars are similar to the brighter quasars at these X-ray
fluxes. Combining with gas column densities inferred from the X-ray
observations we consider the gas-to-dust ratios of the obscuring matter. We
find that the quasars generally have higher gas-to-dust absorption than that
seen in the Milky Way - similar to what has been found for nearby Seyfert
galaxies. We consider the possible existence of a large population of X-ray
sources which have optical properties of Type 1 (unobscured) quasars, but X-ray
properties of Type 2 (obscured) quasars. We show that the observed distribution
of optical-to-X-ray flux ratios of quasars at z>1 is skewed to low values
compared to the intrinsic distribution...
