  About ten years after ferroelectricity was first reported in doped HfO2
polycrystalline films, there is tremendous interest in this material and
ferroelectric oxides are once again in the spotlight of the memories industry.
Great efforts are being made to understand and control ferroelectric
properties. Epitaxial films, which have fewer defects and a more controlled
microstructure than polycrystalline films, can be very useful for this purpose.
Epitaxial films of ferroelectric HfO2 have been much less investigated, but
after the first report in 2015 significant progress has been achieved. This
review summarizes and discusses the main advances on epitaxial HfO2,
considering growth, study of structural and ferroelectric properties,
identification of the ferroelectric phase, and fabrication of devices. We hope
this review will help researchers investigating epitaxial HfO2. It can also
help extend the interest of the ferroelectric HfO2 community, now basically
focused on polycrystalline samples, to epitaxial films.
