  The rank metric measures the distance between two matrices by the rank of
their difference. Codes designed for the rank metric have attracted
considerable attention in recent years, reinforced by network coding and
further motivated by a variety of applications. In code-based cryptography, the
hardness of the corresponding generic decoding problem can lead to systems with
reduced public-key size. In distributed data storage, codes in the rank metric
have been used repeatedly to construct codes with locality, and in coded
caching, they have been employed for the placement of coded symbols. This
survey gives a general introduction to rank-metric codes, explains their most
important applications, and highlights their relevance to these areas of
research.
