Degenerate Higher-Order Scalar-Tensor (DHOST) theories
  This contribution reviews scalar-tensor theories whose Lagrangian contains
second-order derivatives of a scalar field but nevertheless propagate only one
scalar mode (in addition to the usual two tensor modes), and are thus not
plagued with the Ostrodradsky instability. These theories, which encompass the
so-called Horndeski and Beyond Horndeski theories, have recently been fully
classified up to cubic order in second-order derivatives. After introducing
these theories, I present a few phenomenological aspects. In cosmology, these
theories can be included in the unified effective description of dark energy
and modified gravity. Finally, neutron star solutions in some specific models
are discussed.
