The questions of what properties might characterize a solid in two dimensions, and by what mechanism such a solid might melt, are central aspects of current research in condensed matter. Rigorous proofs given in the 1960's showed that truly two‐dimensional systems cannot have the conventional long‐range order typical of three‐dimensional solids. Recent theories have described the types of order that a two‐dimensional solid might possess, including the existence of a nonzero shear modulus.