Hafnia thin films have been under intensive research during the past few years due to its robust ferroelectricity under very thin limit and good compatibility with silicon. The polar crystal structure critical to ferroelectricity in hafnia thin films is metastable, and is generally obtained in polycrystalline thin films, coexisting with other nonpolar phases. Recently, much attention has been focused on epitaxial ferroelectric hafnia thin films to get rid of the nonpolar phases, to investigate the more intrinsic factors to ferroelectricity, and its potential applications. Herein, recent progress on the growth of epitaxial hafnia thin films is reviewed. The epitaxial growth mechanism is explored, in particular, the interface matching, phase stability under temperature and oxygen pressure, followed by discussions on thickness dependency of ferroelectricity, and wake-up effect in hafnia. Finally, an outlook on ferroelectric hafnia both on fundamental studies and future applications is discussed.