  The multiple zeta values (MZVs) possess a rich algebraic structure of
algebraic relations, which is conjecturally determined by two different
(shuffle and stuffle) products of a certain algebra of noncommutative words. In
a recent work, Bachmann constructed a $q$-analogue of the MZVs -- the so-called
bi-brackets -- for which the two products are dual to each other, in a very
natural way. We overview Bachmann's construction and discuss the radial
asymptotics of the bi-brackets, its links to the MZVs, and related linear
(in)dependence questions of the $q$-analogue.
