Freckles looks like a perfectly normal kid. She has bright eyes, a healthy white pelt and gambols happily with Pudding, Sweetie and her five other siblings, exactly as you might imagine young goats do. Until I fend her off, she's very keen on chewing my trousers. To the casual observer, and to goatherds, she shows no signs that she is not a perfectly normal farmyard goat.

But Freckles is a long way from normal. She is an extraordinary creation, an animal that could not have existed at any point in history before the 21st century. She is all goat, but she has something extra in every one of her cells: Freckles is also part spider.

That is what we can now do with genetics: extreme crossbreeding. If 20th-century biology was about taking living things apart to find out how they work, the current era is defined by putting them back together, but not necessarily as evolution decreed, and certainly without the clumsy constraints of mating. Freckles is the result of genetic engineering. But our mastery of manipulating DNA has evolved into an even more extreme form of tinkering, broadly called "synthetic biology". I've been tracking this emerging field since finishing my PhD in genetics 10 years ago, but intensely in the last year as a presenter for the BBC's flagship science strand, Horizon.

Freckles is the creation of Randy Lewis, a professor of genetics at Utah State University. The farm is a university outpost where they research modern farming techniques, teach animal husbandry and raise what are inevitably referred to as "spider-goats".Randy, like many of the other scientists here in Logan, Utah, has farming in his blood. So although a creature that is part goat, part spider might seem like an idea born of science fiction, as far as Randy is concerned it's simply advanced farming: breeding animals to produce things that we want.

"We're interested in dragline silk – the silk that spiders catch themselves with when they fall," he tells me in his midwest lilt. "It's stronger than Kevlar. It really has some amazing properties for any kind of a fibre."

In a sense, spider-goats are an extension of the farming we've been doing for 10,000 years. All livestock and arable has been carefully bred, each cross being a genetic experiment of its own. "The trouble is, you can't farm spiders," Randy says with an almost comic deadpan face. "They're very cannibalistic." He and his team took the gene that encodes dragline silk from an orb-weaver spider and placed it among the DNA that prompts milk production in the udders. This genetic circuit was then inserted in an egg and implanted into a mother goat. Now, when Freckles lactates, her milk is full of spider-silk protein.

We milk Freckles together and process it in the lab to leave only the silk proteins. With a glass rod, we delicately lift out a single fibre of what is very obviously spider silk and spool it on to a reel. It has amazing, and desirable, properties, which is why Randy's seemingly bizarre research is so robustly funded. "In the medical field, we already know that we can produce spider silk that's good enough to be used in ligament repair," he tells me. "We already know we can make it strong enough as an elastic. We've done some studies that show that you can put it in the body and you don't get inflammation and get ill. We hope within a couple of years that we're going to be testing to see exactly the best designs and the best materials we can make from it."

The instructions for all creatures that have ever lived (as far as we know) are written in the code of DNA tucked away in the heart of living cells. Given the bewildering diversity of life on Earth, this system is incredibly conservative. All life is based on an alphabet of just four letters, which, when arranged in the right order, spell out proteins. And all life is made of, or by, proteins. So what this means is that the code for making silk in a spider is written in exactly the same language as the code for making goats' milk.

Since the advent of genetic engineering, we have been able to exploit the universality of this code and cut and paste bits of DNA from any one species into any other. Identifying the genetic basis of all cancers and inherited diseases came from this technology: human or mouse genes have been spliced into bacteria so we could study and experiment on those damaged bits of code. Now, this editing technology has progressed to the extent that all bits of DNA code are effectively interchangeable between all species. In fact, Freckles and the other spider-goats are not even on the cutting edge. The loosely defined field of synthetic biology has come to incorporate even more extreme forms of genetic tinkering.

The most striking headlines so far came when American biologist Craig Venter announced in 2010 that he had created the world's first synthetic life form. Synthia, aka Mycoplasma mycoides JCVI-syn 1.0, was a cell whose genetic code, copied and modified from an existing bacterium, had been assembled not by its parent, but by a computer. That code, including literary quotations and website addresses, was then jammed into the eviscerated chassis of another similar cell and the whole thing booted up. It did live and it hadn't lived before.

But to say that he had "created life" is a stretch that Venter – a master of PR as well as an accomplished scientist – allowed to foment and the press lapped up. It's more accurate to say that he rebooted life, his aim being to create a living template on to which new genetic functions could be built. Nevertheless, it remains an astonishing technical achievement, showing our dominance over DNA; not only can we modify one or two genes, we can make enough to power up a living thing.

The scientists who work in synthetic biology often take a perfunctory, reductionist view of what they do. Massachusetts Institute of Technology professor Ron Weiss is a founding father of this field, a purist who started fiddling with the code of life while coding computers. "I decided to take what we understand in computing and apply that to programming biology. To me, that's really the essence of synthetic biology."

This may sound glib. Life forms are complex at every level. If there is one concrete thing we have learned from the billions spent on reading our own genetic code, it's that biology is messy. Scientists are often confounded by baffling "noise" in the molecules that make up living organisms, unpredictable variation set among unfathomable sophistication. Weiss and his comrades at the BioBricks Foundation want to strip out all the noise in biology and turn it into pure engineering, where organisms can be treated like machines and their inner workings are component parts.

Genes have evolved over millions of years to bestow survival on their hosts by having very specific functions. By standardising these genetic elements in an online registry, anyone can piece them together in any order to create biological circuits with entirely designed purpose. Even the language used is more the stuff of electrical engineering than traditional biology.

"Imagine a program, a piece of DNA that goes into a cell and says, 'If cancer, then make a protein that kills the cancer cell; if not, just go away.' That's a kind of program that we're able to write and implement and test in living cells right now." What Ron Weiss is describing is a study his team published last autumn showing that, by using the logic of computer circuits combined with BioBricks parts, they had built a cancer assassin cell. The logic of the genetic circuit initially distinguishes a cancer cell from a healthy cell using a set of five criteria. It then destroys the tumour cell if it satisfied those conditions. This sniper targeting is the opposite of the blunderbuss approach of chemotherapy, which can destroy both tumour and healthy cells with reckless abandon.

Over the last few years, BioBricks has grown into a global phenomenon. The Registry of Standard Biological Parts currently contains thousands of bits of DNA, all freely available, and this democratisation of science is built into the BioBricks ethos. Every year, undergraduate students compete in an international competition to think of a problem and design and build its solution, using only the parts available in the registry. 2011's European champions, from Imperial College London, designed a system for preventing soil erosion and the conversion of land into desert. There is a remix culture within these teams; it's serious play (the grand prize is a silver Lego brick) and they come from diverse backgrounds – maths, engineering, even astrophysics – unfettered by the narrowly defined science disciplines under which I did my DNA research.

The ease of access to this bleeding-edge technology is breathtaking. Last summer, in suburban Sunnyvale, California, I hung out at a gathering of synthetic biology weekend hobbyists, self-styled as "bio-hackers" with the excellent name BioCurious. There, high-school students were learning about biology by introducing fluorescent proteins from deep-sea jellyfish into bacteria to make them glow in the dark. In 2009, three scientists won Nobel prizes for this work. Already, it is literally child's play.

As with any great revolutions, there are those who stand to make a killing after the doors are kicked open. At the other end of the scale from the open-source, open-access utopia of BioBricks, synthetic biology commercial enterprises are emerging. The tech may be new, but the fields are not. With synthetic biology only a few years old, the most intense areas of commercialised synthetic biology are in fuel and drug production. California biotech companies such as LS9 and Amyris have ploughed millions of dollars into developing synthetic organisms that will produce diesel. In its futuristic labs in Emeryville, Amyris has modified brewer's yeast so that instead of fermenting sugar to produce alcohol, diesel seeps out of every cell. This synthetic biodiesel is already used to power trucks in Brazil. Amyris's ambition is to scale up from pilot plants to industrial-scale production. When I ask chief science officer Jack Newman if they envisage their biofuel replacing natural oil, he is suspiciously coy: "I'll be excited about a billion litres."

One significant fear has less to do with the science and more to do with the shifting balance of economic power. Technology watchdogs and campaign groups such as Friends of the Earth and ETC Group initially called unrealistically for a total ban on synthetic biology, even though it lacked a workable definition. ETC has modified its stance to focus on the industrialisation of these processes, and specifically the fact that synthetic biodiesel organisms need food.

Jim Thomas, who works for ETC, passionately feels that the control of fuel production is simply shifting from one set of corporate giants to another. "Large companies are buying up bits pieces of land so that they can grow sugarcane and then they're feeding it to vats of synthetic microbes to make fuels," he tells me. "Synthetic organisms at this point should not be out there in the environment; they shouldn't be out there in industry. That's irresponsible and inappropriate."

The culture of biology is rapidly changing and scientists and the public need to keep up. Synthetic biology has the potential to generate a new industrial revolution. It is perhaps the defining technology for the 21st century and it is happening now. Without an informed public discourse, fear of this unprecedented and sometimes unsettling technology may hinder the world-changing promise it harbours.

"Prediction is very difficult, especially about the future," as the great physicist Niels Bohr once said. But science fiction never got close to the outlook that came with the advent of synthetic biology. It is now easy to picture a world in which your torn ligaments are replaced with ones made from spider-silk produced by goats; where medicine is served by living programmable machines that seek and destroy only the cells that cause the disease; and where you will drive a car powered by diesel grown by brewer's yeast. Welcome to the future.

Adam Rutherford is a science writer and broadcaster