  We review black hole and star solutions for Horndeski theory. For non-shift
symmetric theories, black holes involve a Kaluza-Klein reduction of higher
dimensional Lovelock solutions. On the other hand, for shift symmetric theories
of Horndeski and beyond Horndeski, black holes involve two classes of
solutions: those that include, at the level of the action, a linear coupling to
the Gauss-Bonnet term and those that involve time dependence in the galileon
field. We analyze the latter class in detail for a specific subclass of
Horndeski theory, discussing the general solution of a static and spherically
symmetric spacetime. We then discuss stability issues, slowly rotating
solutions as well as black holes coupled to matter. The latter case involves a
conformally coupled scalar field as well as an electromagnetic field and the
(primary) hair black holes thus obtained. We review and discuss the recent
results on neutron stars in Horndeski theories.
