  Unconventional superconductivity is commonly linked to electronic pairing
mechanisms, since it is believed that the conventional electron-phonon
interaction (EPI) cannot cause sign-changing superconducting gap symmetries.
Here, we show that this common understanding needs to be revised when one
considers a more elaborate theory of electron-phonon superconductivity beyond
standard approximations. We selfconsistently solve the full-bandwidth,
anisotropic Eliashberg equations including vertex corrections beyond Migdal's
approximation assuming the usual isotropic EPI for cuprate, Fe-based and
heavy-fermion superconductors with nested Fermi surfaces. In case of the
high-$T_c$ cuprates we find a $d$-wave order parameter, as well as a nematic
state upon increased doping. For Fe-based superconductors, we obtain $s_{\pm}$
gap symmetry, while for heavy-fermion CeCoIn$_5$ we find unconventional
$d$-wave pairing. These results provide a proof-of-concept that EPI cannot be
excluded as a mediator of unconventional and of high-$T_c$ superconductivity.
