S.Ev's apartment is about a block away from one of the most interesting stretches of the Berlin Wall. When the East German government closed the border between East and West Berlin in 1961, they did it overnight. Generally they put up barbed wire, but along this stretch of Bernauer Straße, the facades of the apartment buildings were the border.
In those first few days, a bunch of people jumped out their windows - people on the West Berlin side were catching them with blankets and mattresses. After a month or two, the East bricked up the windows, then finally tore down the buildings.
The main Wall memorial is along Bernauer Straße - there's a little museum with pictures and history and some news video of those escapes. (Craziest one: a grandma already most of the way out of her window, but with East German police pulling her back in while West Germans are pulling her out. She made it out.) They've also reconstructed part of the wall:
This is the view from the west - the wall was way more than just the big famous concrete blocks that face the west. There's another wall facing the east, and there's the death strip in the middle. Border guards shot to kill, although some people argue they weren't all that careful about their aim. But still, more than 200 people died trying to escape over the Berlin Wall. (Many more died along the main border between East and West Germany.)