  In this review we focus our attention on scalar-tensor gravity models and
their empirical verification in terms of black hole and wormhole physics. We
focus on a black hole, embedded in an expanding universe, describing both
cosmological and astrophysical scales. We show that in scalar-tensor gravity it
is quite common that the local geometry is isolated from the cosmological
expansion, so that it does not backreact on the black hole metric. We try to
extract common features of scalar-tensor black holes in an expanding universe
and point out the gaps that must be filled.
