Since the crew of Apollo 17 returned from the moon in December 1972, no human has ever left low-Earth orbit. Five space shuttles, scores of Russian Soyuz capsules, the International Space Station, and more than 450 men and women have left the Earth since Apollo, but all have been bound to a small shell of space just outside our atmosphere.

Any hope of an ambitious successor to Apollo might have been abandoned altogether if it wasn't for George W Bush. In 2003, he announced plans for Nasa to return to the moon by 2020 and then travel on to Mars by 2030. Once again, though, the US faces some serious competition. The same year that Bush tasked Nasa with the 21st century moonshot, Yang Lee Wei became China's first astronaut and, explicit or not, another space race had begun.

"The attitude to the space programme in China is a little bit like the attitude towards space exploration in the western world in the 1960s," says Kevin Fong, an expert in space medicine at University College London. "There's a deep fervour among their university kids for space technology. The main difference between China and America now is that China can just do something - they don't need to ask permission or go through a democratic process and get the budget approved."

This means that China can progress its space programme quickly; if it wants to land on the moon - and many observers think it does - the country could do it well ahead of 2020, the earliest possible date for an American return.

China's only confirmed plans so far include launching another robotic orbiter to the moon, probably followed by a robot lander and perhaps a lunar rover. Beyond that, we might not find whether China wants to put a person on the moon until it does it. Its successes are broadcast all over the world, but its failures remain internal. That hasn't stopped serious people taking it seriously, though: last year the former Nasa administrator, Mike Griffin, said he believed China had the capability to get to the moon and he wouldn't be surprised if the next person to walk on the moon was Chinese.

"It's all very dark out there and you're not really sure how much they're doing," says Fong. "They seem very serious about it and have mature thoughts about it, from the little you see in their presentations. They still have much to learn from the existing space community and don't want to be too overt about their ambitions at risk of looking like they've over-promised."

The Indians are also hot on the heels of the US. India worked on an embryonic space programme with the Soviet Union in the 1970s and flew its first cosmonaut in 1982. Today the budgets are relatively big - around $800m a year and a 10-year plan for human spaceflight that has committed funding of more than $1.2bn. It has already sent a robotic probe to the moon, but there is still plenty to prove in terms of human spaceflight - the country has indicated bold ambitions but has still not revealed any confirmed details that it will send people into orbit, never mind all the way to the moon.

The Chinese and the Indians have many advantages over the Americans of the 1960s - they are starting well ahead of Apollo in terms of technology. But it might not be technology that decides the winner. Aiming for space is about more than understanding flight paths and knowing the best rockets to use: moon shots are about taking risks. Fong points out that the Apollo programme prioritised mission objectives over life or limb. No one was complacent about the danger, he says, but since most of the astronauts were former test pilots, they understood that things can - and would - go wrong. The modern Nasa has inverted this priority - today the astronauts' lives are absolutely more important than mission goals. This will have to change if Nasa is to return to the moon and, particularly, if it wants to send people to Mars. And perhaps here China will have a clear advantage over the US.

And what about the Brits? This country has a fantastically successful (if largely invisible) robotic space industry. And, against all the odds, it has its first official astronaut in the shape of Tim Peake, an army helicopter test pilot. Despite providing no funds for human spaceflight, science minister Paul Drayson is optimistic that a British astronaut could one day walk on the moon. "I hope so," he says. "We're absolutely committed to space research, both manned and unmanned. It's hugely aspirational and extremely challenging and helps us put things in perspective."