Light travels in the nearest possible thing to a straight line. But a black hole bends time and space so much that the nearest thing to a straight line is a curved path leading into the black hole.

Black holes are quite good at sucking: "According to Einstein's theory of general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including electromagnetic radiation (e.g. visible light), can escape its pull after having fallen past its event horizon. The term derives from the fact that absorption of visible light renders the hole's interior invisible, and indistinguishable from the black space around it." Source and further information: http://en.wikipedia.org/wiki/Black_hole ----- ADDED (for an explanation) ---- "Two concepts introduced by Albert Einstein are needed to explain the phenomenon. The first is that time and space are not two independent concepts, but are interrelated forming a single continuum, spacetime. This continuum has some special properties. An object is not free to move around spacetime at will; it must always move forward in time and cannot change its position in space faster than the speed of light. This is the main result of the theory of special relativity. The second concept is the base of general relativity; mass deforms the structure of this spacetime. The effect of a mass on spacetime can informally be described as tilting the direction of time towards the mass. As a result, objects tend to move towards masses. This is experienced as gravity. This tilting effect becomes more pronounced as the distance to the mass becomes smaller. At some point close to the mass, the tilting becomes so strong that all the possible paths an object can take lead towards the mass. This implies that any object that crosses this point can no longer get further away from the mass, not even using powered flight. This point is called the event horizon." Source and further information: http://en.wikipedia.org/wiki/Black_hole

E=mc^2

Well, what with matter and energy being proven to be equated, and the affects of acceleration and time dilation being provable, observable phenomena, it's easy to understand how the curvature of the space-time continuum affects light, both as a particle and as a wave function.

Photons (light) are considered massless particles -- zero rest mass. Classically (in Newton's view) anything with zero mass should not be affected by gravitational fields -- even from a black hole. But when Einstein's theory of relativity is applied (as it must) then photons have a tiny effective mass m associated with their energy E by E=mc^2. So light rays are observed to be slightly bent as they go past our Sun, and greatly bent by black holes. Inside a black hole's event horizon, light is trapped by this small mass associated with its energy -- it can't get out.

7-9-2017 The black hole is imaginary. Isaac Newton proved that the net gravitation at the center of a body is zero, so the basic notion of a black hole, that is crushes itself by gravity, is impossible. Chemists find that protons and neutrons can only clump together in certain combinations called "islands of stability". Get off by even one particle and the clump flies apart. So the notion of neutronium is disproved. Even in the sloppiest scenario, a black hole can exist only if it is the only object in the universe. A second object would distort the black hole by its gravity and it would no longer stay together.