The Finnish elevator's walls are bathed by a blue luminescence; music that is not quite jazz gently tootles within.

But the elevator's dozen or so buttons seem numbered at random: 45, 105, 215, 270. At level 350, the doors hiss open on a dark and dirty cavern.

Germany's highest meeting room, 600 miles to the southwest of that Finnish elevator, has its oddities, too. It looks out not at a central business district, but on the bucolic edge of the Black Forest. It sits atop a skyscraper which contains no offices but 12 elevator shafts. In the elevator by which you reach the penthouse, an indicator tells you not just what floor you are headed for, but how fast you are getting there.

ThyssenKrupp, a German engineering conglomerate, and Kone, a Finnish elevatormaker, are two of the world's big four elevator-engineering companies. As such, they need places to test new designs, new patterns of operation and new technologies. Kone does this in a mineshaft in Tytyri, a few miles west of Helsinki; if you take that glowing blue elevator down to the dank cavern at level 350 — so called because it is 350 meters (1,150 feet) below the top of an adjacent shaft — and go through a steel door you will find yourself in the working mine which that other shaft serves.

ThyssenKrupp's facility is more flashy; a slim, 246-meter-high concrete finger clad in an elegant barley-sugar twist of fabric. Inaugurated in October, it towers above the medieval town of Rottweil, Germany, hitherto best known for its beefy guard dogs.

The technology being improved in these out-of-the-way places is essential to modern city life. Around 1 billion people take one of the world's 14 million elevators each day; they take twice as many elevator journeys in a day as people take flights in a year. Cities struggle on through bus and rail strikes; life without elevators, at least in central business districts, would more or less grind to a halt. Most cities reach for the sky, sometimes dramatically — Dubai — sometimes in a higgle-piggle — São Paulo.

The elevator is to the vertical what the car is to the horizontal: the defining means of transport. Like cars, modern elevators are creatures of the second industrial revolution of the late 19th century. Like cars, they have transformed the way that cities look, changing how and where people live and work. And today, like the cars that are moving toward an autonomous future, elevators stand ready to change the city again.

The rise of the big four

By the 1970s, elevator engineering was a pretty mature industry, and started to consolidate and globalize. Kone and ThyssenKrupp, along with the Swiss firm Schindler, bought up rival firms to join Otis (now a division of United Technologies) as worldwide brands. Between them the big four now account for around two-thirds of the global market; Hitachi and Mitsubishi Electric of Japan take quite a lot of the rest. There is as yet no Chinese elevator giant — perhaps because the industry relies as much on its ability to provide services on a global scale as on its mechanical engineering prowess. Half the big four's annual revenue of $40 billion come from that side of the business.

But if China is not a force in the industry, it has been a huge influence on it; the Chinese appetite for more, higher and faster elevators is like nothing seen since 1920s New York. In 2000, 40,000 new elevators were installed in the country. By 2016 the number was 600,000 — almost three quarters of the 825,000 sold worldwide. China not only wanted more skyscrapers; it wanted taller ones. More than 100 buildings around the world are over 300 meters; almost all of them were built this century, and nearly half of them in China.

Such buildings exacerbate the constraints elevatormakers and the architects they work with have always faced: time and space. Kheir Al-Kodmany at the University of Illinois has found that after 28 seconds waiting, would-be passengers start to get irritated. And while elevators make rentable floor space reachable, they attract no rent themselves. At the top of the tallest buildings (which are often tapered, both because of the wind and to reduce loading on the structure below) the elevator shafts may take up 40 percent of the floor space. The fewer the shafts, the more lucrative the building.

Really tall buildings pose problems of their own. Dubai's Burj Khalifa, the tallest building in the world, has 163 floors and measures 830 meters to its tip. But to get to the top you must change at a sky lobby; the longest ride offered by any of its 57 elevators is just 504 meters. The limiting factor is the steel elevator cable. Any longer and it gets so heavy that it might snap under it own weight.

UltraRope, developed by Kone, gets around this problem by using carbon fiber. When the Jeddah Tower in Saudi Arabia, the world's first 1,000-meter building, opens in 2020 it will boast a 660-meter elevator made possible by UltraRope.

A development being tested at Rottweil goes even further — doing away with the cable. ThyssenKrupp, which also makes railway equipment, has harnessed high-speed rail technology to create Multi, a system held in place and accelerated by electromagnetic forces like those used for magnetic-levitation trains. This is not a new idea. One of the first people to look into it was a Ph.D. student in Manchester, England, in the 1970s, Haider al-Abadi, who is now prime minister of Iraq. But now it seems as if its time may have come.

Rethinking the future

By eliminating the cable, Multi aims to take away all limits on height other than those imposed by a building's structure. The absence of cables will also allow elevators to move laterally, as well as vertically, making the whole system more like a railway. Elevator shafts will be able to fork and rejoin to allow overtaking; descending elevators could sidestep ascending ones.

The first building to commission such elevators, Berlin's East Side Tower, is awaiting certification by the authorities, probably around 2020.

Adrian Godwin, a consultant, imagines systems like Multi making buildings of 250 stories or more possible. Buildings could change shape, as well as size. New types of sideways-scooting elevators could link up whole clusters of buildings. Transport hubs could house elevators serving a range of local buildings, moving first horizontally, then vertically. Or the elevators could zip between their tops on skybridges. Having let cities climb into the sky, the elevator may now help them spread across it.