Recently, the Budapest-Marseille-Wuppertal collaboration achieved sub-percent precision
in the evaluation of the lowest-order hadronic vacuum polarization contribution to the muon $g_\mu-2$.
At this level of precision, isospin-symmetric QCD is not sufficient.
In this contribution we review how QED and strong-isospin-breaking effects have been included in our work.
Isospin breaking is implemented by expanding the relevant correlation functions to second order in the electric charge $e$
and to first order in $m_u-m_d$.
The correction terms are then computed using isospin-symmetric configurations.
The choice of this approach allows us to better distribute the available computing resources among the various contributions.