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You've pretty much got it with our current understandings Alex. The event horizon is the point at which the escape velocity reaches the speed of light. This means that anything that approaches the event horizon doesn't so much fall into the blackness as much as slowly reddens and fades away. This happens more so with smaller black holes than super massive ones as the gravitational gradient is larger in smaller ones that bigger ones.
What is on the other side of the event horizon is still a guess. The most well accepted theory is that of a singularity which is a point in space of infinite density. Think of everything inside the event horizon being squashed being crushed into a volume smaller than a quark or an electron. A single point of infinite mass and density.
The problem is that we don't really know what happens on the other side of the event horizon so there is every chance that there is another kind of degenerate matter that we're not aware of that stops total collapse. White Dwarfs are held against collapse from electrons not willing to get too close. Once there is too much gravity they're pushed closer together and eventually it is the unwillingness of neutrons to get too close (Neutron Stars). Maybe there is a quark degenerate matter that? Who knows.
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