  A latin square of order $n$ is an $n\times n$ array of $n$ symbols in which
each symbol occurs exactly once in each row and column. A transversal of such a
square is a set of $n$ entries such that no two entries share the same row,
column or symbol. Transversals are closely related to the notions of complete
mappings and orthomorphisms in (quasi)groups, and are fundamental to the
concept of mutually orthogonal latin squares.
  Here we provide a brief survey of the literature on transversals. We cover
(1) existence and enumeration results, (2) generalisations of transversals
including partial transversals and plexes, (3) the special case when the latin
square is a group table, (4) a connection with covering radii of sets of
permutations. The survey includes a number of conjectures and open problems.
