  Kohn-Sham density functional theory (DFT) has become established as an
indispensable tool for investigating aqueous systems of all kinds, including
those important in chemistry, surface science, biology and the earth sciences.
Nevertheless, many widely used approximations for the exchange-correlation (XC)
functional describe the properties of pure water systems with an accuracy that
is not fully satisfactory. The explicit inclusion of dispersion interactions
generally improves the description, but there remain large disagreements
between the predictions of different dispersion-inclusive methods. We present
here a review of DFT work on water clusters, ice structures and liquid water,
with the aim of elucidating how the strengths and weaknesses of different XC
approximations manifest themselves across this variety of water systems. Our
review highlights the crucial role of dispersion in describing the delicate
balance between compact and extended structures of many different water
systems, including the liquid. By referring to a wide range of published work,
we argue that the correct description of exchange-overlap interactions is also
extremely important, so that the choice of semi-local or hybrid functional
employed in dispersion-inclusive methods is crucial. The origins and
consequences of beyond-2-body errors of approximate XC functionals are noted,
and we also discuss the substantial differences between different
representations of dispersion. We propose a simple numerical scoring system
that rates the performance of different XC functionals in describing water
systems, and we suggest possible future developments.
