  We compute the boundary terms and junction conditions for Horndeski's
panoptic class of scalar-tensor theories, and write the bulk and boundary
equations of motion in explicitly second order form. We consider a number of
special subclasses, including galileon theories, and present the corresponding
formulae. Our analysis opens up of the possibility of studying tunnelling
between vacua in generalized scalar-tensor theories, and braneworld dynamics.
The latter follows because our results are independent of spacetime dimension.
