  A quasi-infinitely divisible distribution on $\mathbb{R}^d$ is a probability
distribution $\mu$ on $\mathbb{R}^d$ whose characteristic function can be
written as the quotient of the characteristic functions of two infinitely
divisible distributions on $\mathbb{R}^d$. Equivalently, it can be
characterised as a probability distribution whose characteristic function has a
L\'evy--Khintchine type representation with a "signed L\'evy measure", a so
called quasi--L\'evy measure, rather than a L\'evy measure. A systematic study
of such distributions in the univariate case has been carried out in Lindner,
Pan and Sato \cite{lindner}. The goal of the present paper is to collect some
known results on multivariate quasi-infinitely divisible distributions and to
extend some of the univariate results to the multivariate setting. In
particular, conditions for weak convergence, moment and support properties are
considered. A special emphasis is put on examples of such distributions and in
particular on $\mathbb{Z}^d$-valued quasi-infinitely divisible distributions.
