Two-dimensional melting

For a decade now the subject of the nature of the two-dimensional melting transition has remained controversial. An elegant theory based on the unbinding of pairs of crystal defects suggested that two-dimensional solids might melt by a transition sequence involving two continuous transitions separated by a novel, nearest-neighbor-bond-orientationally ordered fluid---the hexatic phase. Competing theories predict that the transition is of the usual first-order type observed in three-dimensional systems. This paper is a critical review of the current status of research into the problem of two-dimensional melting, with an emphasis on computer simulations. An attempt is made to point out unresolved issues pertaining to this fascinating and still open question.