It has been almost 14 years since the last supersonic airliner last flew. From 1976 to 2003 the Concorde brought supersonic air travel to the public, but now NASA has plans to bring back supersonic flights.
One limitation for supersonic flights is that the FAA bans flying over the speed of sound over land due to the disrupting and damaging effect of sonic booms. This limited the Concorde to transatlantic flights only, severely limiting its consumer base to international flights.
NASA plans to combat this major drawback by designing an airplane that is able to fly at supersonic speeds but creates as small of a shockwave as possible in order to reduce the size and power of the sonic boom. On the ground, the sonic boom would only be a soft thump or low rumble rather than the glass-breaking explosion that is normally produced. This would allow it to be flown over land, dramatically increasing the number of possible flights and destinations the aircraft could travel.
NASA plans on spending $390 million over the next five years on developing this new aircraft. This new plane will fly two to three times faster than the current airliners and will get you from New York to LA in three hours.
There still are the economic hurdles of making these aircraft successful in the long run, however. The design of this type of aircraft is possible, but it still has to make a profit. It has to be fuel efficient as well as carry enough passengers to make it economically viable.
This video explains some of the difficulties that this new supersonic plane will have to face in order for it to be successful.