Helium crystals exhibit faceting as do ordinary crystals, but no other crystals can grow and melt sufficiently fast to make the propagation of crystallization waves possible at their surfaces. After nearly two decades of controversy, it is now generally accepted that helium crystals are model systems for the general study of crystal surfaces, but also exceptional in having unique quantum properties. This review, which summarizes 25 years of research on the surface of helium crystals, treats both what is general and what is particular to helium. A central issue among the general properties is the “roughening transition,” the phase transition from a smooth faceted state of the crystal surface at low temperature to a rough and fluctuating state at high temperature. This review describes the series of experiments that have significantly improved our understanding of this transition and its related critical phenomena. Some attention is paid to the experimental techniques, which are rather unusual in many cases. The Nozières renormalization theory of roughening is also described in some details and compared with experiment. Other general properties of crystal surfaces have also been studied in helium, such as the energy of steps on the facets and their mutual interactions, and several instabilities. The relevant experiments are presented together with their theoretical interpretation. The quantum mechanisms that control the growth dynamics of helium crystals are also reviewed. Here, too, theory is compared with experiment, not only in the matter of crystallization waves, but more generally on the mass and heat flows in nonequilibrium situations, including the two stable helium isotopes ${}^4\mathrm{He}$ and ${}^3\mathrm{He}$, which behave in quite different ways. Finally, a list of open questions is presented for future research.

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