**Brane-World Gravity** Roy Maartens and Kazuya Koyama summarize the concept of brane-world gravity, which posits that our observable universe is a 1+3-dimensional brane embedded in a higher-dimensional bulk spacetime. Gravity is free to propagate into the bulk, while Standard Model particles and fields are confined to the brane. This framework arises from M theory, which unifies gravity with other fundamental forces. The 1+10-dimensional M theory includes the 1+9-dimensional superstring theories and is considered a promising approach to quantum gravity. At low energies, gravity is localized on the brane, recovering general relativity, but at high energies, gravity "leaks" into the bulk, altering gravitational dynamics. This has significant implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a way to test predictions of M theory, such as modifications to general relativity. The review focuses on warped 5-dimensional brane-worlds based on the Randall–Sundrum (RS) models, which use a negative bulk cosmological constant to confine gravity. The RS 1-brane model, with a single brane, and the RS 2-brane model, with two branes, are discussed. The 5-dimensional Dvali–Gabadadze–Porrati (DGP) models are also analyzed, where gravity is modified at low energies. The review also covers 6-dimensional models with co-dimension two branes. The RS models are derived from 5D Einstein equations and junction conditions. The 5D graviton's KK modes are analyzed, showing how gravity is localized on the brane. The RS 1-brane model provides a new approach to the hierarchy problem, where the effective Planck scale on the brane is much larger than the fundamental scale. The RS 2-brane model introduces radion stabilization and potential collider signatures. The review also discusses the Kaluza–Klein (KK) modes of the graviton, showing how extra dimensions affect gravity. The RS models are shown to have a unique geometric structure, with the bulk being a portion of anti-de Sitter (AdS) spacetime. The AdS/CFT correspondence is discussed, linking the bulk gravitational dynamics to the boundary conformal field theory. The review covers the geometry, dynamics, and perturbations of brane-world models, including gravitational collapse, black holes, and cosmological perturbations. It also discusses the implications of brane-world gravity for cosmology, such as inflation and the early universe. The review concludes with a discussion of the broader implications of brane-world models for understanding quantum gravity and the nature of spacetime.**Brane-World Gravity** Roy Maartens and Kazuya Koyama summarize the concept of brane-world gravity, which posits that our observable universe is a 1+3-dimensional brane embedded in a higher-dimensional bulk spacetime. Gravity is free to propagate into the bulk, while Standard Model particles and fields are confined to the brane. This framework arises from M theory, which unifies gravity with other fundamental forces. The 1+10-dimensional M theory includes the 1+9-dimensional superstring theories and is considered a promising approach to quantum gravity. At low energies, gravity is localized on the brane, recovering general relativity, but at high energies, gravity "leaks" into the bulk, altering gravitational dynamics. This has significant implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a way to test predictions of M theory, such as modifications to general relativity. The review focuses on warped 5-dimensional brane-worlds based on the Randall–Sundrum (RS) models, which use a negative bulk cosmological constant to confine gravity. The RS 1-brane model, with a single brane, and the RS 2-brane model, with two branes, are discussed. The 5-dimensional Dvali–Gabadadze–Porrati (DGP) models are also analyzed, where gravity is modified at low energies. The review also covers 6-dimensional models with co-dimension two branes. The RS models are derived from 5D Einstein equations and junction conditions. The 5D graviton's KK modes are analyzed, showing how gravity is localized on the brane. The RS 1-brane model provides a new approach to the hierarchy problem, where the effective Planck scale on the brane is much larger than the fundamental scale. The RS 2-brane model introduces radion stabilization and potential collider signatures. The review also discusses the Kaluza–Klein (KK) modes of the graviton, showing how extra dimensions affect gravity. The RS models are shown to have a unique geometric structure, with the bulk being a portion of anti-de Sitter (AdS) spacetime. The AdS/CFT correspondence is discussed, linking the bulk gravitational dynamics to the boundary conformal field theory. The review covers the geometry, dynamics, and perturbations of brane-world models, including gravitational collapse, black holes, and cosmological perturbations. It also discusses the implications of brane-world gravity for cosmology, such as inflation and the early universe. The review concludes with a discussion of the broader implications of brane-world models for understanding quantum gravity and the nature of spacetime.