# Horndeski theory and beyond: a review

## TL;DR

This review comprehensively discusses recent advances in Horndeski and generalized scalar-tensor theories, highlighting their applications in cosmology, astrophysics, and modifications of general relativity, including observational constraints and black hole solutions.

## Contribution

It provides a systematic overview of the development, extensions, and phenomenological implications of Horndeski theory and its generalizations in modern gravity research.

## Key findings

- Horndeski theory unifies scalar-tensor models of gravity.
- Cosmological perturbations in Horndeski theory inform structure formation.
- Black hole solutions with scalar hair are explored within these frameworks.

## Abstract

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.