What happens to light and mass in the center of a black hole?

It's difficult to know what happens on the other side of a black hole, since no information can cross back through the event horizon (the radius at which light and therefore any information can no longer escape). The leading idea is that near the center of every black hole lies a singularity, or a point where the density (and therefore the curvature of space-time) reaches infinity (that is, some amount of mass contained in zero volume).

Any mass which crosses the event horizon will accelerate inwards toward the singularity. When it starts to get close, it will experience tremendous tidal stress. Because the singularity contains the mass of anywhere from one supergiant star to several million of them (or possibly more) and is infinitely dense, the end of the object which is closer to the singularity will experience significantly more gravitational force than the end facing away. This will manifest itself as a gradually increasing stretching of the mass, something colloquially referred to as "spaghettification."

The falling mass will contact the singularity and become part of it in finite time in the reference frame of the mass. To an outside observer, things get a little funny due to the relativistic effects of such a strong gravitational field. Beyond the event horizon, time is essentially frozen, so to anyone watching the black hole, nothing can ever happen inside it. So if an object starts to get close to it and fall in, it will gradually slow down and turn red (the light is red-shifted) and never cross the horizon. The light will get more and more red-shifted until it is infrared, microwaves, radio waves, etc--until it essentially disappears. But you will never observe it cross the horizon. The object itself will cross the horizon normally, however it will still always look like it hasn't crossed the horizon--because all light is rushing down towards the singularity, and none can come back the other way, it will always appear that the horizon is just beyond reach. Looking the other way though, the outside world would appear extremely weird once inside the horizon.

I would argue that there are no theories about what happens to anything in the center of a black hole, that there are only hypothesis. But that's just a nit-pick about the wording.

Nobody knows what happens inside a black hole, but yes, lots of scientists have guessed about what might happen. The most common idea is probably the one mentioned in the other answer, that everything is pulled into a singularity, where all the energy occupies a single point at the center. A common assumption in this case is that the information in the energy is then destroyed since it is basically homogenized.

Other than that, use your imagination. Whatever you can dream up might happen to stuff in the center of a black hole, some physicist has probably thought of it and tried to determine its feasibility.

One idea that I like was presented in an article in the Scientific American magazine a year or two ago. This article suggested that perhaps a black hole isn't really hole-like at all, and it presents a hypothesis that suggests that the mass of a collapsing neutron star has enough of a push outward to stop its total collapse just before it enters what would be its own event horizon, thereby making it more of a "black star." In this case, the supposed black hole is just a lump of hyper-dense matter, similar to a neutron star but even denser.