What is the name of the theory that describes gravity as curvature of spacetime?

The theory that describes gravity as curvature of spacetime is general relativity. Albert Einstein published the completed theory in 1915, and it was formally presented in 1916 as a new description of gravitation.

In general relativity, matter and energy change the geometry of four-dimensional spacetime. Objects such as planets then follow the straightest possible paths through that curved geometry, which we observe as gravity. This replaced Newton's idea of gravity as an instantaneous force, while reproducing Newton's predictions in weak gravitational fields and at low speeds.

The theory explains effects that Newtonian gravity cannot fully account for, including gravitational time dilation, the bending of light, gravitational redshift, black holes, and the small extra shift in Mercury's orbit. A common mix-up is with special relativity: special relativity describes motion, space, and time without gravity, whereas general relativity extends relativity to gravity and acceleration.

General relativity remains the standard theory of gravity for planets, stars, galaxies, and the large-scale universe. Its predictions have been repeatedly tested, including through observations of gravitational lensing, binary pulsars, and gravitational waves.