  The shape-controlled synthesis of cuprous oxide (Cu$_2$O) photocatalysts with
both low or high index crystal planes has received increasing attention due to
their unique facet-dependent properties. Since they are cheap and earth
abundant, these well-defined Cu$_2$O nanostructures are extensively used for
different photocatalytic reactions, also because of their strong visible light
absorption capability. However, further development will be still needed to
enhance the efficiency and photostability of Cu$_2$O, which still limits its
industrial application. We start this review by summarizing the synthetic
advancement in the facet engineering of Cu$_2$O and other associated hybrid
Cu$_2$O-based heterostructures with a special emphasis put on their growth
mechanism. We then discuss different facet-dependent properties, which are
relevant to photocatalysis. In the subsequent section, we present a critical
discussion on the photocatalytic performance of faceted Cu$_2$O nanostructures
during organic synthesis, hydrogen production, and carbon dioxide
photoreduction. The relation between photocatalytic efficiency and product
selectivity with exposed crystal facets or with different composition of hybrid
nanostructures is also discussed. Finally, important strategies are proposed to
overcome the photostability issue, while outlining the course of future
development to further boost the technological readiness of well-defined
Cu$_2$O-based photocatalysts.
