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The Horndeski action is the most general one involving a metric and a scalarfield that leads to second order field equations in four dimensions. Being thenatural extension of the well known Scalar-Tensor theories, its structure andproperties are worth analysing along the experience accumulated in the lattercontext. Here we argue that disformal transformations play, for the Horndeskitheory, a similar role to that of conformal transformations for Scalar-Tensortheories a l`a Brans-Dicke. We identify the most general transformationpreserving second order field equations and discuss the issue of viable framesfor this kind of theories, in particular the possibility to cast the action inthe so called Einstein frame. Finally, we investigate the physical equivalenceof such frames and their reciprocal relationship.

Disformal invariance of second order tensor-scalar theories: framing the Horndeski action