In a Penrose diagram:

A detailed exposition, complete with animated spacetime diagrams, on how the Penrose diagram of the Schwarzschild geometry is constructed can be found at More about the Schwarzschild Geometry on the Falling into a Black Hole website.
The Penrose diagram shows that the horizon is really two distinct entities, the Horizon, and the Antihorizon. The Horizon is sometimes called the true horizon. It's the horizon you actually fall through if you fall into a black hole. The Antihorizon might reasonably called the illusory horizon. In a real black hole formed from the collapse of the core of a star, the illusory horizon is replaced by an exponentially redshifting image of the collapsing star. As the collapsing star settles towards its final nohair state, its appearance tends to that of a nohair black hole.
This animated gif (12K) version of the Penrose diagram illustrates light rays that start from the Antihorizon, or from the Horizon, and hit the observer. The diagram shows that when you look at a black hole from the outside, you are looking at its Antihorizon, or illusory horizon. When you fall through the horizon, you fall not through the Antihorizon, but rather through the Horizon, or true horizon. The Horizon becomes visible only after you have fallen through it. The Antihorizon continues to remain ahead of you, and you never fall through it.
However, the Schwarzschild geometry has a simple mathematical form, and that form can be extended analytically. The mathematical extension consists of a second copy of the Schwarzschild geometry, reversed in time, glued along the Antihorizon. The complete analytic extension of the Schwarzschild geometry contains not only a Universe and a Black Hole, but also a Parallel Universe and a White Hole. This is simply a mathematical construction, with no basis in reality. Still, it is cute that even the simplest kind of black hole, a Schwarzschild black hole, harbors alien mathematical passageways.
This animated gif (90K) version of the Penrose diagram illustrates how an infaller sees infinitely bright, infinitely blueshifted bursts of light:

I've given the various regions and horizons of the ReissnerNordström spacetime names. General relativists do not commonly name all the pieces this way, and they might not agree with my naming choices.
As illustrated by its Penrose diagram, the topology of an extremal ReissnerNordström black hole differs from the standard ReissnerNordström topology. For this reason and others, it is thought that an extremal ReissnerNordström black hole cannot be constructed, even in principle, by adding charge to a standard ReissnerNordström black hole. Indeed, adding charge to a nearextremal black hole takes energy, which increases the mass of the black hole, keeping it subextremal.
The mathematical solutions for superextremal ReissnerNordström black holes, those with charge exceeding mass, have no horizons at all, which is an even more drastic change in topology.
Real charged particles such as electrons and protons have charge greatly exceeding their mass. For example, an electron has a chargetomass of e/m_{e} ≈ 10^{21} (the ratio of the square root of the fine structure constant to the electron mass in Planck units). However, the character of such particles is dominated by quantum mechanics, not by classical general relativity.