Here's a look at how the area has changed since the Korean War, courtesy of web forum Daum (via KoreaBang). Originally, the area was called Youngdong, but since then, it's become known as Gangnam.
The photos below, you can see UN tanks in Gangnam's Sinsa-dong and rice paddies. By the 1960s, roads and bridges helped provide the infrastructure necessary for the area's growth to take off. By the 1970s, there are blocks of apartments that make a marked contrast with the rural fields that surrounded them.
However, the Gangnam of today really started to emerge around the 1988 Seoul Olympics, as the Games helped create even more rapid, and impressive, urbanization. The Trade Tower, viewable above, was built in 1988 and is one of the country's tallest buildings.
The images below show just how far Gangnam has come in the last sixty (or so) years with much of the most explosive growth occurring in the last few decades.