  We provide a framework for relating certain q-series defined by sums over
partitions to multiple zeta values. In particular, we introduce a space of
polynomial functions on partitions for which the associated q-series are
q-analogues of multiple zeta values. By explicitly describing the (regularized)
multiple zeta values one obtains as $q\to 1$, we extend previous results known
in this area. Using this together with the fact that other families of
functions on partitions, such as shifted symmetric functions, are elements in
our space will then give relations among (q-analogues of) multiple zeta values.
Conversely, we will show that relations among multiple zeta values can be
`lifted' to the world of functions on partitions, which provides new examples
of functions where the associated q-series are quasimodular.
