It was first proposed in 1919 by Sun Yat-Sen, a Chinese political leader and finally in 2009, the dam started to create hydroelectricity. Later, 6 new power generators were added in 2011 and in 2012, the project was deemed complete.
It went through a lot of ups and downs, protests, ownership chnages etc over the years but eventually came through.
It generates a massive 22 GW of hydroelectric power. To give an idea about how big that is, only 35 countries in the world have installed capacity bigger than that. Even a country like Singapore has installed capacity lower than that.
It's a true engineering marvel...Take a look at one of the turbines.
By Voith Siemens Hydro Power Generation (http://www.voithsiemens.com) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons