A quasi-infinitely divisible distribution on ℝ^d is a probability distribution μ on ℝ^d whose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible distributions on ℝ^d. Equivalently, it can be characterised as a probability distribution whose characteristic function has a Lévy–Khintchine type representation with a “signed Lévy measure”, a so called quasi–Lévy measure, rather than a Lévy measure. A systematic study of such distributions in the univariate case has been carried out in Lindner, Pan and Sato (Trans Am Math Soc 370:8483–8520, 2018). 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 ℤ^d -valued quasi-infinitely divisible distributions.