  This article is intended to review the recent developments in the Horndeski
theory and its generalization, which provide us with a systematic understanding
of scalar-tensor theories of gravity as well as a powerful tool to explore
astrophysics and cosmology beyond general relativity. This review covers the
generalized Galileons, (the rediscovery of) the Horndeski theory, cosmological
perturbations in the Horndeski theory, cosmology with a violation of the null
energy condition, degenerate higher-order scalar-tensor theories and their
status after GW170817, the Vainshtein mechanism in the Horndeski theory and
beyond, and hairy black hole solutions.
