Why are walls always straight? Why does it cost so much to build them? And why do big construction projects so often run late? Construction has always been a conservative industry, used to doing things how they have always been done.

But a new wave of innovation is coming, which will change what buildings look like, how they are made, and who wins in the new era of the construction industry.

Architects have always been limited by what their builders can actually make. But if robots were doing the building, all sorts of new possibilities open up.

Straight walls partly exist for the convenience of builders and architects - but for a robot, a curved wall is almost as easy. So at the DFAB House, a small test building in the suburbs of Zurich, Switzerland, the main wall follows an elegant, irregular curve. It’s built around a steel frame, welded by robots, which humans would have found almost impossible to construct unaided.

Even stranger, the roof consists of a series of flowing, organic ridges, which look as if they were secreted by a giant insect. Awkward to dust, perhaps, but designed by computer and made with 3D printing to achieve the same strength as a conventional, straight roof, yet with half the weight.

The house, built by Switzerland’s National Centre of Competence in Research in Digital Fabrication, demonstrates what a computer-designed, robot-built house could look like.

For instance, SAM, the “semi-automated mason” developed by a US company called Construction Robotics, has been used on a number of construction projects in the US. It can lay an accurate course of bricks with mortar, but still needs a human tender to measure the site, set up the robot and tidy up the external surface of the mortar afterwards.

And while these may open up exciting new design possibilities, their biggest impact will be on the economics of building projects.

When the earth is first moved at the start of a construction project, it will often now be under digital guidance. The Japanese company Komatsu now sells diggers equipped with GPS technology which know, to within a centimetre or two, exactly where the bucket edge is scraping the ground.

But construction sites are not ideal environments for high-tech kit. They are dirty, messy, and full of unpredictable things - humans, vehicles, and the weather. So in the short term at least, robots may make their biggest contribution away from the construction site itself.

The top floors of the DFAB House were built by two robots which never went outdoors. Mounted on the ceilings of a large factory space, they worked together to cut, drill and position the wooden of the frame, and they were delivered by truck.

This form of building, now known as “off-site” or “modular” construction is becoming far more widespread. Once known as “prefabricated building”, it was associated with poor quality, cheaply constructed buildings, such as those built in the UK to house people made homeless after World War Two.

But prefab is making a comeback across the world. In Singapore, the government hopes to have a third of new homes built by the government’s Housing and Development Board made with prefabricated units, in a bid to increase construction productivity by 25%.

Rooms are constructed precisely out of concrete in factories, painted, wall covers and floorings applied, and windows and bathrooms fitted, before being assembled into buildings on site.

But prefabrication is not just a way to make boring grey apartments a bit cheaper. Disruptive companies are using it as way to deliver new buildings to the highest design and environmental standards at affordable prices.

In Reno, Nevada, Ukrainian-born Maxim Gerbut’s firm ivDom is updating the concept of prefabrication for the 21st Century.

Manufactured out of plastic composites using its own 3D printing technology, its mobile houses are 36 sq m (387 sq ft) in area, and exceed the most exacting standards of energy efficiency, called “ivhaus”. This enables them to stay heated and lit by solar s alone, with no connection to the grid.

Mr Gerbut jokingly calls it the “zombie-proof house”, as so little heat or sound escapes that undead monsters who rely on those senses to find prey would have no idea that anyone was inside.

And prefabrication will make it possible to build them relatively cheaply, in places far from mains power and water, where construction labour would be tough to find.

Compared with vehicle manufacturing, construction is a highly fragmented industry, which has been slow to adopt new technologies and ideas. But that has begun to change.

Building firms are under pressure to be less wasteful, and to deliver buildings which are more environmentally friendly and cheaper to run.

Meanwhile, the promise of greater efficiency is looking too tempting to resist. The consulting firm McKinsey estimates that technology could cut 20-40% of the cost of construction projects.

That creates a glittering prize for any firm that can capture it, says Jose Luis Blanco, a partner at McKinsey, who advises big construction firms.

“Whenever you see a disruption like the one we see coming here, you always see a huge value pool being created. That value pool is not going to be divided equally amongst the people that are now players.

“What I can tell you with certainty is that not everyone that is here right now is going to be here in five or ten years’ time.”

After decades of crawling along on in the technological slow lane, the industry is waking up to the impact that new ways of building will bring.

Many builders are looking at the world through digital eyes and thinking, “Why do we do it this way?”. And the future they see for us will be very different.