Horndeski's theory of gravity (the most general scalar-tensor theory with

second-order equations of motion) has recently attracted considerable

attention as a framework to study gravitation and cosmology. I will review

some features of these theories, including recent efforts to understand their

cosmological signatures and the posibility of making them compatible with

local gravity tests (by means of screening mechanisms). Then I will challenge

the generality of Horndeski\'s theory as the most general, physically

reasonable scalar-tensor theory by considering derivative couplings to

matter. When expressed in the Jordan frame, these theories have higher

derivative equations of motion but introduce no additional, ghostly degrees of

freedom. Theories beyond Horndeski have unique characeristics and

represent a new class of scalar-tensor theories of gravity.