  The product of two zero mean correlated normal random variables, and more
generally the sum of independent copies of such random variables, has received
much attention in the statistics literature and appears in many application
areas. However, many important distributional properties are yet to be
recorded. This review paper fills this gap by providing the basic
distributional theory for the sum of independent copies of the product of two
zero mean correlated normal random variables. Properties covered include
probability and cumulative distribution functions, generating functions,
moments and cumulants, mode and median, Stein characterisations,
representations in terms of other random variables, and a list of related
distributions. We also review how the product of two zero mean correlated
normal random variables arises naturally as a limiting distribution, with an
example given for the distributional approximation of double Wiener-It\^{o}
integrals.
