There have been numerous attempts to modify general relativity, with either the motivation to account for dark energy or to model quantum gravity effects. Scalar-tensor theories have often played a prominent role in these attempts and recently special attention has been devoted to scalar-tensor theories whose Lagrangians contain second-order derivatives of a scalar field (like Horndeski theories, mimetic gravity and also Horava gravity in some sense...). In this seminar, I will present how one can classify Higher-Order Scalar-Tensor theories which propagate only one scalar degree of freedom in addition to the usual tensorial modes. I will also discuss applications in cosmology.