Physicist: Terrible, terrible things.
The first thing you’ll be likely to notice as you approach the hole is the tidal forces. Tidal forces are nothing more than the difference in gravitational force between the near and far side of an object, and they aren’t particular to blackholes. For example, the tidal force of the moon on the Earth causes tides (hence the name). For any reasonable sized blackhole (less than thousands of suns), the tidal force between different parts of your body will be greater than your body’s ability to stay intact, so you’ll be pulled apart in the up-down direction. For much more obscure reasons, you’ll also be crushed from the sides. These two effects combined are called “spagettification”. Seriously. Assuming that you somehow survive spagettification, or that you’re falling into an super-massive blackhole (which is ironically much more gentle than a smaller blackhole) then you can look forward to some bizarre time effects.
It’s been established for decades that “time moves slower the lower”. For example, GPS satellites have to deal with an additional 45 microseconds every day due to their altitude (they move through time faster). Also, one way to think about gravity is as a “bending” of the time direction downward. In this way anything that moves forward in time will also naturally move downward. At the event horizon of a blackhole (the outer boundary) time literally points straight down. As a result, escaping from a blackhole is no more difficult than going back in time. Once you’re inside all directions literally point toward the singularity in the center (since no matter what direction you move in will be toward the future).
We don’t experience time moving at different rates or being position dependent, so when we start talking about messed up spacetime it’s useful to look at things from more than one point of view.
From an outsider’s perspective (far from the blackhole): As someone falls in they will move slower and slower through time. They will appear redder, colder, and dimmer. As they approach the event horizon their movement through time will halt, as they fade completely from view. Technically, you’ll never actually see someone fall into a blackhole, you’ll just see them get really close.
From an insider’s perspective (falling into the blackhole): First, torn apart and crushed. Things farther from the blackhole move through time faster, so the rest of the universe will speed up from your point of view. As a result the rest of the universe becomes bluer, hotter, and brighter. The blue shift of the incoming light turns it into gamma rays. So, right before you pass through the event horizon, you’ll get nuked with a universe’s lifetime worth of starlight and microwave background radiation turned into nuking nastiness. The event horizon itself is only special from an outside perspective. If you fall in you should pass right through it. However, what you see in the moment that you pass through the horizon is dependent on things we don’t know yet.
-If the blackhole lasts until the universe ends (assuming that the universe ends), then you’ll see the entire history of the universe whip by (bluely). You’ll then find yourself face to face with the singularity. At that point you go away, according to the math. However, the universe is slippery like a greased up eel fresh from the bar exam. It always finds a way to not have singularities where the math predicts it. So, to be safe, I’ll say “no one knows what happens then”.
-If the blackhole evaporates, then all the matter that (almost) gets to the horizon will be torn apart and reappropriated as Hawking radiation. If you were to survive, then you would find yourself as close to the horizon as (for uncertainty reasons) it is possible to be, and you would ride it in as it shrinks. In a blink you’d suddenly find yourself floating around right next to an amazing explosion, as the last of the blackhole evaporates.