Add to ORKGInternational audienceThis 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