The Reichenbach Fall

We watched Sherlock plummet to his death.
We know he survived. The question remains - How did he do it?
This is what we think happened.

Images from St Barts and additional theories added!

Steven Moffat, in an interview, mentioned that the clue to the fall was something rather uncharacteristic Sherlock did in the episode but something most people missed. For people who have read the books, his treatment of the reporter - when he says "You repel me" – is hardly like Sherlock. He's merely very blunt but factual – not mean on purpose. That was an opinion and Sherlock is far too indifferent to form personal opinions of people. And sure enough - lots of people think so. In fact, the idea most of them gather is that the word of relevance is "rappel". The basic idea is that Sherlock uses a bungee rope during the fall to decelerate him enough before impact such that he’s relatively unharmed and then poses as the body to deceive Watson.

We need to remember that Sherlock was prepared to feign a suicide and that the arrangements he made were in accordance with the idea that Moriarty himself would also need to be deceived, should it come to that. Because no matter how you slice it, the opinion that Sherlock could have foreseen Moriarty’s suicide holds no water.

So he uses a bungee attached to some part of the roof, but strictly not visible to anyone on the roof itself. In all likelihood, something attached just under the roof and positioned such that he could grab the same as soon as he falls. We need to be clear on the fact that the bungee is attachable and not held on to by him, because the visuals would contradict such an idea. When he’s close enough to the ground, i.e. out of Watson’s line of sight, he detaches the bungee and hits the ground. Needless to say, Sherlock would have ensured that given his weight, the bungee decelerates to a velocity low enough for him to hit the ground without sustaining significant damage.

Post impact, most things do not change from the original idea. The crowd around his body is essentially comprised of the Baker Street irregulars (the homeless network, to those unfamiliar with the books), the person knocking down Watson also being a part of the same. And by doing so, he gives Sherlock the time to get blood on his face and impersonate a dead body. Also, the fact that Watson isn’t allowed to properly take a pulse becomes especially noteworthy in that light. As for Molly, Sherlock requires her to possibly falsify DNA records to ensure his death is verified and/or to confirm the same – since she’s a mortician or coroner at St. Barts.

On to the interesting bit –proof! Slow down (.25x - 1:23:25 onwards) - the bit where the sniper aiming at Watson draws the pointer away and you notice as he scrolls up, a piece of rope/string near the ceiling. It's not conclusive but it is easily the most blatant clue in the episode if the theory holds!

Potential Problems

Pace of the episode
The episode is so fast, in terms of the depiction of the fall that you don't see any time for a break in the fall. And frankly, Moffat and co. are too smart to bother with trying to mess with the depiction of time - which is why I think most theories of the person falling not being Sherlock don't hold much water. The idea that things happen after the fall make much more sense because we see Watson being run to the ground for a considerable period of time. However, no one is speculating about the fall itself! In any case, a break will only take so much time so that's no reason to rule it out.
Presence of a rope or harness
The fall depiction has no ropes or string anywhere in view - but given that movies do this sort of thing on a regular basis, without the attachment being visible unless you look really hard, I don't see this as a deal breaker. While this is mostly done with editing, it has been pointed out to me that sometimes, such procedures are done using camouflaged ropes which are surprisingly effective. So again, plausible to ignore.
A 'repel-sive' theory
The idea that ‘repel’ leads to rappel which also isn’t an accurate description of the theory, in afterthought, appears to be a long shot.
A red herring
This isn’t exactly the problem but it’s obvious that Sherlock is leading us somewhere when he tightens the scarf before his fall. I’m inclined to think that this is a feeble attempt at misleading audiences to deduce the idea of a dummy who replaces him post the fall.
The Final Problem
The final problem (no pun intended!) is that when the sniper draws away and you see the rope - you realize he's moving away from the direction of the point from which Sherlock should have fallen. That is assuming Watson is looking at the point where Sherlock fell when the sniper draws away. Sherlock has been taken away by now and Watson appears to have turned 180 degrees so this might just be in the favour of the theory.

submitted by @KushagraUdai

Next: Alternate Theories