  Surface freezing is a phenomenon in which crystallization is enhanced at a
vapor-liquid interface. In some systems, such as $n$-alkanes, this enhancement
is dramatic, and results in the formation of a crystalline layer at the free
interface even at temperatures slightly above the equilibrium bulk freezing
temperature. There are, however, systems in which the enhancement is purely
kinetic, and only involves faster nucleation at or near the interface. The
first, thermodynamic, type of surface freezing is easier to confirm in
experiments, requiring only the verification of the existence of crystalline
order at the interface. The second, kinetic, type of surface freezing is far
more difficult to prove experimentally. One material that is suspected of
undergoing the second type of surface freezing is liquid water. Despite strong
indications that the freezing of liquid water is kinetically enhanced at
vapor-liquid interfaces, the findings are far from conclusive, and the topic
remains controversial. In this perspective, we present a simple thermodynamic
framework to understand conceptually and distinguish these two types of surface
freezing. We then briefly survey fifteen years of experimental and
computational work aimed at elucidating the surface freezing conundrum in
water.
