Annie Lowrey's New York Times Magazine article on how Washington got so rich and can it stay this way in an era of austerity is a great read.
But since the article deals with both the larger metropolitan area and also the city in particular, I think it's worth putting the growth of the District itself in some context. The chart above, drawn from Census figures, shows the share of the American population residing in the District of Columbia over the past hundred years or so. What you can see is that in the first half of the twentieth century, the nation's capital became more prominent and that the New Deal and World War II in particular turned the United States into a more capital-centric country. But since that time it's essentially been a long slide.
So you have to ask yourself, what is it that's really in need of explanation here. If you heard about a country with a growing economy and a growing population, and then you heard that the population and economy in its capital city is also growing you'd thing "fair enough." But DC's population actually shrank enormously between between 1950 and 2000 (despite, I hasten to add, a continual expansion in federal government spending) with the city losing about 25 percent of its residents. Census Bureau estimates suggest that in the two years since the 2010 Census, the city really has grown rapidly and once again contains 0.2 percent of the American population just like it did back in 2000. If we keep growing faster than the nation at large, it's easy to imagine us re-obtaining our 1990 or 1980 share of national population but to ever return to being home to 0.4 percent of the American population as we were in 1940 seems unimaginable. A more interesting question is whether the city's zoning authorities will ever allow us to once again contain 800,000 people as we did way back in 1950.
Which is just to say that DC growth should be put in perspective. In the 40 years after 1970, Houston added 900,000 people. DC has fewer than 700,000 people overall. That is a city that's growing rapidly.
Washington, I would say, is mostly a city that's snapping back from a combination of negative technology shocks (the automobile is very useful but was a huge blow to cities with a lot of pre-car infrastructure), very bad policy choices, and the national crime wave of the 1970s and 80s. It's true that the DC suburbs in Virginia are growing very rapidly. But the suburbs of Atlanta and Charlotte and other southern cities are also growing very rapidly. Ask yourself how quickly the affluent suburbs of New York and Boston would grow if they had developer-friendly sunbelt politics as seen in Virginia or North Carolina?