  We explore the theory of multiple zeta values (MZVs) and some of their
$q$-generalisations. Multiple zeta values are numerical quantities that satisfy
several combinatorial relations over the rationals. These relations include two
multiplicative relations, which arise naturally from comparison of the MZVs
with an underlying algebraic structure. We generalise these concepts by
introducing the parameter $q$ in such a way that as $q\to 1^-$ we return to the
ordinary MZVs. Our special interest lies in two $q$-models recently introduced
by H. Bachmann. He further conjectures that the $\mathbb{Q}$-spaces generated
by these $q$-generalisations coincide. In this thesis we establish a particular
case of Bachmann's conjecture.
