The observable universe is described as a 1+3-dimensional "brane" embedded in a higher-dimensional "bulk," where gravity can access the bulk while Standard Model particles and fields remain confined to the brane. This framework, rooted in M-theory, suggests that at high energies, gravity behaves in a higher-dimensional way, leading to significant changes in gravitational dynamics and perturbations. These changes have implications for high-energy astrophysics, black holes, and cosmology. The review focuses on warped 5-dimensional brane-world models based on the Randall–Sundrum (RS) models and the 5-dimensional Dvali–Gabadadze–Porrati (DGP) models, which modify gravity at low energies. It also covers 6-dimensional models with co-dimension two branes. The review analyzes the geometry, dynamics, and perturbations of these models, providing a phenomenological framework to test novel predictions and corrections to general relativity implied by M-theory.The observable universe is described as a 1+3-dimensional "brane" embedded in a higher-dimensional "bulk," where gravity can access the bulk while Standard Model particles and fields remain confined to the brane. This framework, rooted in M-theory, suggests that at high energies, gravity behaves in a higher-dimensional way, leading to significant changes in gravitational dynamics and perturbations. These changes have implications for high-energy astrophysics, black holes, and cosmology. The review focuses on warped 5-dimensional brane-world models based on the Randall–Sundrum (RS) models and the 5-dimensional Dvali–Gabadadze–Porrati (DGP) models, which modify gravity at low energies. It also covers 6-dimensional models with co-dimension two branes. The review analyzes the geometry, dynamics, and perturbations of these models, providing a phenomenological framework to test novel predictions and corrections to general relativity implied by M-theory.