  We find spherically symmetric and static black holes in shift-symmetric
Horndeski and beyond Horndeski theories. They are asymptotically flat and
sourced by a non trivial static scalar field. The first class of solutions is
constructed in such a way that the Noether current associated with shift
symmetry vanishes, while the scalar field cannot be trivial. This in certain
cases leads to hairy black hole solutions (for the quartic Horndeski
Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term).
Additionally, we find the general spherically symmetric and static solutions
for a pure quartic Lagrangian, the metric of which is Schwarzschild. We show
that under two requirements on the theory in question, any vacuum GR solution
is also solution to the quartic theory. As an example, we show that a Kerr
black hole with a non-trivial scalar field is an exact solution to these
theories.
