  We present the data-driven reconstruction of gravitational theories and Dark
Energy models on cosmological scales. We showcase the power of present
cosmological probes at constraining these models and quantify the knowledge of
their properties that can be acquired through state of the art data. This
reconstruction exploits the power of the Effective Field Theory approach to
Dark Energy and Modified Gravity phenomenology, which compresses the freedom in
defining such models into a finite set of functions that can be reconstructed
across cosmic times using cosmological data. We consider several model classes
described within this framework and thoroughly discuss their phenomenology and
data implications. We find that some models can alleviate the present
discrepancy in the determination of the Hubble constant as inferred from the
cosmic microwave background and as directly measured. This results in a
statistically significant preference for the reconstructed theories over the
standard cosmological model.
