What boundary marks the point beyond which nothing can escape a black hole?

The event horizon is the boundary beyond which nothing can escape a black hole.

It is not a solid surface. Instead, it is a region in spacetime where the escape speed would exceed the speed of light. Because relativity sets light's speed as the ultimate speed limit, anything crossing the horizon can no longer send a signal back to the outside universe.

The event horizon is different from the singularity, which is the central region predicted by classical general relativity, and from the accretion disk, which is hot matter orbiting outside the black hole. A distant observer does not see an object visibly cross the horizon because light from the object becomes increasingly delayed and redshifted.

The horizon's size depends on the black hole's mass. For a nonrotating black hole, its radius is called the Schwarzschild radius. Rotating black holes have a more complicated structure, but they still possess an event horizon.