I'd think that on certain heavily trafficked routes, especially ones with lots of business travelers, there would be a market for high-speed (supersonic) flights?
Why are there currently no supersonic commercial flights? (Or are there?)
There a several reasons for the demise of commercial supersonic aircraft. And there is a strong possibility we may be able to take a ride on a supersonic aircraft by 2021.
Supersonic commercial aircraft have a lot of constraints on them which are not present on subsonic commercial aircraft and which military aircraft are not subject to.
Supersonic aircraft - and in particular high supersonic and hypersonic aircraft - are considerably more expensive to design and manufacture as they require the use of novel materials and manufacturing techniques in their design. As you pass about Mach 2, heat starts to become a major problem, weakening traditional aerospace aluminum alloys to the point that they are no longer a viable material to construct an aircraft from. The airframes also expand and contract considerably in the heat and this must be accounted for in the design. Designers are forced to seek out more exotic materials like Titanium alloys, high temperature composites, etc. and it is not just structure that requires novel materials to address this - fuel systems, electrical wiring, mission systems, even sealants and paint all must be chosen so as to combat heat but still satisfy traditional design metrics like safety, durability, and economics.
The result of this are very high development costs: Adjusted for inflation, Concorde costs the governments of England and France some $28 billion or roughly 5 1/2 times the cost that Boeing spent to develop the 747. Similar figures were consumed on the design and development of the ill fated Boeing 2707, which never progressed past the mockup stage, even after re-design.
Super Sonic Transport (or SST) design favors a slender, needle-like fuselage which limits the number of people which the jet can carry. The Concorde was limited to approximately 100 passenger in very narrow seats; the 2707 could carry 260 people but had a length of over 300 feet making it very awkward and unruly in existing terminal aprons or taxiways. This also makes the SST very unprofitable for its operators, as Concorde proved. Over the last 50 years no more than 20 SSTs have ever been operational and all with only three airlines - British Airways, Air France, and the Soviet Aeroflot - all of which were heavily subsidized by their respective governments.
Design of SSTs have in the past been hampered by the high fuel consumption rates of turbojet engine imposing a design range limit of approximately 4,500 NM. This effectively curbs sales to airlines looking for SSTs to fly the pacific rim routes where the times savings offered by a supersonic aircraft would be the most pronounced.
Supersonic aircraft generate noxious sonic booms which can cause damage to fragile structures on the ground and generally are a nuisance to the inhabitants below. While advancements in quiet supersonic transports are happening, global aeronautical regulation bodies still prohibit supersonic flight over land, restricting an SST to subsonic flight over these regions, making its operation exponentially more expensive than a traditional subsonic aircraft.
A high speed SST would be required to operate in the higher parts of the stratosphere in excess of 60,000 feet. While this is achievable for military pilots in full pressure suits, there are considerable risks to civilians in street clothes at these altitudes should a rapid decompression occur. At these heights a rapid decompression will boil your blood inside your veins (very painful way to die). It also cannot be combated with traditional supplemental oxygen systems, making such a scenario very dangerous for passengers.
The 'dirty burning' turbojet previously discussed create a lot of NOX emissions, far more that today's high bypass turbofans, which poses risk of increased depletion of stratospheric ozone.
A conventional high bypass turbofan subsonic airliner is between 16-20 times more efficient on a cost per passenger per NM basis. A typical transatlantic ticket on a 747-8 is approximately 1500 USD. A ticket on the Concorde was about 11,000 in today's dollars.
Taken all together and faced with the reality of designing such a craft with 3 million parts, 6 million lines of software code, all tested and validated, which is restricted only to transatlantic routes, aircraft designers quickly see the handwriting on the wall and the aircraft is doomed from the drafting paper upward.
But that's not to say the supersonic dream is dead. Aerion in Reno, NV and Airbus are in the process of developing a 16 passenger supersonic business jet, capable of Mach 1.6, with a tentative rollout and flight in 2021. Areion claims the jet will have a 'boomless' cruise up to Mach 1.2 at or above FL350 and hopes this will coax regulating bodies into permitting supersonic flight over land. Whether this attracts enough customers willing to pay the estimated $100 million price tag per aircraft remains to be seen.
There are numerous reasons. They are not all economic ones by the way, even if most of them are.
Neither of the two supersonic airliners that once flew fly anymore, and none of the aircraft that still exist are likely to made airworthy ever again.
Someone's going to have to design and build a new one.
The British and French governments began collaborating in earnest on the project in the late 1950s. The immediate post-war period was over, but they both faced a kind of crisis as their colonial empires fell apart across the world, making for just the kind of mood in which weakening global powers reach for grand projects that will prove that they really are, after all, in the top club of nations.
For slightly different reasons at the same time the USA and the USSR were also making huge efforts to prove themselves Top, expressed in the race to reach the moon.
It was at any rate a moment that seemed to demand extraordinary symbolic achievements in technology by certain governments.
Now, no government has the stomach for that kind of project, nor do their populations (one wonders whether China or India might soon decide that it's time for their grand gesture though). International agreements, such as those that bind the member states of the European Union as well as trade agreements that reach across the world, limit the kind of support governments can provide to enterprises of this scale, that made them possible in the past.
They don't seem to be able to keep their own airlines going any more, never mind global-scale technological extravagances.
So if the 21st century is no longer a time for such politically-powered technological extravagance, it's going to be up to private enterprise to produce it, and now the economic factors start to become more important.
Time spent in the air is not "dead time" for the highly-expensive business traveller any more. Increasingly, in-flight Internet and telephone connections will make it less urgent to be there now. The business traveller will be more interested in comfort and facilities, if the flight time can be used productively.
A supersonic airliner will be fuel-expensive. Since the 1970s, the price of oil has fluctuated violently enough several times to cause various airline-related extinctions. Airlines flying supersonic airliners will take the first hit.
Airlines already face a great deal of pressure because of environmental concerns: it's an industry that's hugely damaging to the planet.
A supersonic airliner will be considerably more damaging than most.
Which airline is likely to want to be the first to fly the most environmentally-noxious airliner in the world in order for the super-rich to spend a little less time getting wherever it is they go?
It's far from clear that any airline could afford to invest in a supersonic fleet, and it would have to earn a vast amount of money even if they could.
Where would it fly? One thing that the Concorde project failed to foresee was just how obnoxious the aircraft were to the people who lived anywhere near their noise.
For a while the British and French put up with the appalling noise it made because it reassured them that they were still great, but after a while even they grew pretty tired of it.
The Americans cared rather less about Franco-British greatness, and kept trying to ban it from the USA; it was banned from flying over various other places too.
Let's assume that you could build a supersonic airliner that was civilised enough to be reasonably welcome at airports near populous cities (and Concorde with its 1960s turbojets would not be), you'd still have an aircraft that could not be flown over populated land at supersonic speeds, because of the horrific noise its shockwave would make.
So, it would be pretty much limited to coast-to-coast operations over oceans.
There's not just one reason why we haven't seen a new supersonic passenger airliner, but a whole raft of them - and I think it will be a very long time before we do.
There are regulations in place that state that a supersonic aircraft can only go supersonic when over sea, (especially seen with concerns about noise levels when concorde was in production, and sonic booms 'breaking windows' when flying over land) and must be subsonic when on land, which limits the amount of destinations you could get supersonic flights to (like if you were travelling from Turkey to France), not to mention that supersonic jets guzzle fuel (especially delta winged design ones, such as Concorde and the TU-144, which need extra thrust on takeoff due to the design making it harder to gain lift).
They're very expensive to maintain as a whole, which can be seen by the amount of wear that can be done during supersonic flight, which is costly to repair, and if oil prices go up, it adds onto that expense because of how much it guzzles. If there's a demand for people to fly supersonic, then considering there's limited routes to do so, it would just make a supersonic jet a tin can of losses.
In addition to @DanieleProcida's great points, there is one more very significant factor affecting demand: long-range private jets.
Supersonic airliners only provide a speed benefit to passengers traveling between the cities directly served. Once you have to connect (and go through customs and immigration, plus the inevitable schedule padding to minimize the risk of that causing missed connections), the end-to-end speed of the trip drops dramatically. A long-range private jet can take you directly from origin to destination with no connection/layover time, and customs and immigration for GA aircraft is usually very fast. Private jets can operate at much smaller GA airports that are likely to be much more convenient to the passengers, and there's no check-in lines or security theater adding time to the trip either. They can also leave as soon as you get on board, rather than on a fixed schedule, though it is harder to calculate the dollar/time value of that. And they're usually a heck of a lot more comfortable, with no worries about screaming kids and such--unless you brought your own.
Chartering a private jet is expensive, but one ticket on Concorde was in the same ballpark, and the private jet is definitely cheaper if several people are traveling together.
Although Concorde was still in good flying condition and a stellar plane, when it was retired from service in 2003, it had been 34 years since it's first flight using technology that was first proposed in the 1950's There's simply not many planes that are still flying in commercial aviation that are more than 30 years old.
There's lots of reasons why supersonic transport never caught on. The reasons are far too many to list here and the most relevant ones have been covered in other answers. It gets down to economics. Neither the Tu-144 or the Concorde made economic sense beyond the limited routes they flew, which hampered anticipated sales.
Since the time the Concorde made it's first flight, there has been dramatic improvements in aerodynamics, electronics, engines and building materials. Most of the developments in aeronautics have been directed at improving planes flying below mach 1 for better fuel efficiency and noise reduction. Some of those developments would work well for supersonic flight. Issues like sonic booms can be dramatically reduced which gives hope for overland flights. In some scenarios, the booms are reduced to 1% of what Concorde generated. If the planes can fly from New York to Seattle, then onto Tokyo, or trans Europe and Asia, it opens up entirely new markets that Concorde could not fly.
There have been efforts to bring back supersonic travel. Twenty years ago, Boeing proposed a faster plane, the Sonic Cruiser which would carry up to 250 passengers and have a sweet spot just below Mach 1 and just above Mach 1 and be much more economical to run. Commercial airlines didn't want extra speed so much as they wanted a plane that was cheaper to fly. This is how we ended up with the Boeing 787 Dreamliner instead.
However, there are several air-frames in development that are capable of supersonic flight. My strong feeling is that supersonic is coming back.
First off, Boeing never let the Sonic Cruiser concept die. I don't think they ever let go of the idea of a supersonic plane like the the Boeing 2707. Last year they announced a concept passenger plane capable of Mach 5.
For the last twenty years, EADS — the parent company of Airbus announced that it was considering working with Japanese companies to develop a larger, faster replacement for Concorde. The concept is a plane that carries 300 passengers at Mach 2 with a per-seat ticket price comparable to flying subsonic speeds. No firm plans have been announced.
Lockheed would like to get back into commercial aviation and has been working with Supersonic Aerospace International on a Quiet Supersonic Transport. This plane would seat 12 passengers, cruise at Mach 1.6 and create a sonic boom only 1% as strong as that generated by Concorde. It is also working with NASA on the X-59 QueSST.
Boom Technology is an American startup company designing a Mach 2.2 (1,300 kn; 2,300 km/h) 55-passenger supersonic transport with 4,500 nm (8,300 km) of range, to be introduced in 2023, called Overture. Boom is hoping to power the Overture with three moderate bypass turbofans without afterburners, unlike Concorde's Rolls-Royce/Snecma Olympus. The issue is finding a non-military efficient engine. Boom is working with Japan Airlines and Virgin to develop a plane that could make a flight from San Francisco to Tokyo in under 6 hours.
There are other planes in development. I think we are within five years of seeing supersonic planes capable of trans-atlantic, trans-pacific flights which should open up entire new markets for supersonic planes.