How do black holes bend light around them?

Black holes bend light through gravitational lensing, a consequence of Einstein's general relativity. Mass warps the fabric of spacetime, and light follows the curved geometry of that spacetime rather than traveling in a straight line. The more massive the object, the more severely spacetime curves, and the more dramatically light paths bend. Near a black hole, this effect becomes extreme. At the photon sphere, roughly 1.5 times the Schwarzschild radius, gravity is strong enough that light can actually orbit in circles. Closer than that, toward the event horizon, the curvature becomes so intense that light cannot escape at all. This is why black holes appear black despite bending surrounding light into dramatic arcs and rings visible to outside observers.