  We summarize our recent results for the quark loop part of the light-by-light
scattering contribution as well as the hadronic vacuum polarisation
contributions to the anomalous magnetic moment of the muon. In particular we
focus on the role played by the momentum dependence of the quark- and
quark-photon vertex dressing functions. We give a detailed comparison of the
Dyson-Schwinger description of this contribution to the corresponding picture
emerging from hadronic models in particular the extended Nambu--Jona-Lasonio
model (ENJL). We find that the details of the momentum dependence are important
on a quantitative level. Especially the transverse parts of the
quark-photon-vertex, which serve as a dynamical extension of simple vector
meson dominance models, do not yield the large suppression of the
light-by-light contribution found in the ENJL model if realistic dressings are
taken into account.
