[TL;DR Transoceanic flights may become 4x faster in a decade]
Aerospatiale/BAC Concorde (Mach 2)
Operated between 1976 and 2003 the Concorde is still the fastest airliner in the history of humankind. Due to a number of complications including notorious accidents the program was cancelled, however ambitions for supersonic travel have not died.
21st Century Supersonic
Boom Supersonic
Virgin Galactic
NASA
US Air Force
Blackbird SR-71 (Mach 3.2)
Operated between 1964 and 1998, the Blackbird is still the most impressive plane ever practically utilized. To carry out long range reconnaissance missions the Blackbird flew at 85,000 feet (25,900 meters) at over Mach 3.2 making the plane near impossible to hit with surface-to-air missiles. These extreme circumstances made the plane notoriously difficult to operate, but it played an essential role in the Cold War.
X-Planes (Mach 5 - 10)
In collaboration with NASA, USN (US Navy), DARPA (Defence Advanced Research Projects Agency), and USMC (US Marine Corps), the US tests experimental planes since the 1940s. The purpose of this is to provide proof of concepts for new aerospace technologies, without the expectation that the prototypes will go into full-scale production.
North American X-15 (Fastest aircraft with human on board)
On 3 October 1967 the X-15 achieved Mach 6.7 for a brief period of time.
NASA X-43A (Fastest autonomous aircraft)
In March 2004 the X-43A achieved Mach 9.64 momentarily.
Boeing X-51 (Fastest sustained autonomous aircraft)
On 1 May 2013 the X-51 achieved Mach 5 for 210 seconds.
Hypersonic Air Travel (Mach 5+)
Hermeus
A new start up based out of Atlanta, Georgia (home of Georgia Tech: one of the best aerospace engineering departments in the world). Recently acquired US$100 million in funding and has won a US$950 million ceiling ABMS contract with USAF.
Chimera Engine
Quarterhorse (Small Autonomous Aircraft)
Darkhorse (Mid-Size Autonomous Aircraft)
Halcyon (Passenger Aircraft)
Undisclosed Challenges
Fuel economy/sustainability
Air friction/extreme heat/hull durability
Acceleration/deceleration phases
Airspace regulation