For decades, health researchers across the world have known that athletes enjoy a significantly lower risk of cancer than the rest of us.
Large studies have shown how they suffer markedly fewer cancers of the lungs, kidneys, breasts, ovaries and cervix.
Investigators have in the past suggested that there may be a simple explanation: athletes eat more healthily and are less likely to smoke.
But now there is evidence showing that in fact it is exercise itself that protects our bodies against cancer in complex ways.
Furthermore, for patients who have cancer, exercise may significantly boost their chances of survival. Nor do you have to be a champion athlete to reap these benefits.
Danish researchers say that adrenaline, which gets released when we exercise, is a key to the protective effect.
The Copenhagen University Hospital doctors injected cancer cells into two groups of mice. The first had activity wheels on which they could run as much as they liked. The second group had no exercise other than moving inside their cages.
Dr Pernille Hojman, the oncologist who led the study, says that when the mice were exposed to a chemical known to cause liver cancer, only a third of the exercise group developed tumours compared with three-quarters of the non-exercisers.
Furthermore, the tumours that did grow in running-wheel mice were around 60 per cent smaller than those in their sedentary counterparts.
When Dr Hojman studied the tumours in the exercising mice, she found that they contained more infection-combating cells than the sedentary animals' cancers.
From this, she discovered that a type of immune defence cell called a natural killer cell was fighting cancers in the exercising mice.
Adrenaline is known to power our natural killer cells. And another exercise-induced chemical, interleukin-6, helps these immune cells to target tumours. When Dr Hojman's team injected adrenaline and interleukin-6 into cancerous sedentary mice, the rodents' immune systems attacked the tumours as effectively as if they had been exercising regularly.
Writing in the journal Cell Metabolism, Dr Hojman said that the combined hormone therapy could help people who are too old or too ill to be active to get some of the cancer-fighting benefits of physical exertion.
However, she is quick to downplay the idea that "exercise in an injection" could help those who are merely lazy, as exercise carries other important anti-cancer benefits.
Crucial among these is the power of exercise to reduce inflammation, the body's mechanism for fighting infections. But as we age, our defences become increasingly prone to producing excess inflammatory chemicals.
Numerous studies have demonstrated how chronic inflammation can damage the DNA inside our cells, making them significantly more likely to turn cancerous.
Chronic inflammation has also been found to raise the risk of some tumours, such as breast cancer, recurring.
Australian researchers reported in the journal Breast Cancer Research & Treatment earlier this year that gentle weight-training can significantly lower inflammation levels in women who don't normally exercise.
They studied 39 women who had survived breast cancer and found that when the women exercised three times a week, the levels of inflammatory chemicals in their bodies dropped significantly - which should reduce the risk of the disease recurring.
Exercise also appears to stimulate the release of another tumour-fighting substance - the brain chemical dopamine, say Chinese scientists.
They found that when mice with liver cancer were made to swim regularly in moderate amounts, levels of dopamine increased in their bodies. The tumours in these mice shrank.
The researchers reported in the journal Oncogene that when they gave the mice a drug that blocked the action of dopamine, the cancer-fighting benefits of moderate exercise disappeared.
They also found that when the mice were made to swim excessively, the protective effect of exercise disappeared - perhaps due to physical exhaustion. Regular exercise has another, more obvious effect - weight loss and losing body fat is a way of reducing our risk of cancer.
In March, a European consortium of exercise scientists conducted a review of existing research and concluded that having fat deposits around the stomach raises the risk of cancers of the stomach and oesophagus, liver, biliary tract, and leukaemia.
In women, fat tummies also raised their risk of kidney, bladder and colorectal cancers, the investigators reported in Cancer Causes & Control journal.
The charity Cancer Research UK is funding a trial of 50 men who have early, slow-growing prostate cancer to see if exercise delays the progress of their cancers.
Half the men in the study will do 2½ hours of aerobic exercise every week for 12 months, initially supported by trainers. The other half of the men will be given information about the benefits of exercise for cancer patients, but will not have supervised sessions.
Dr Liam Bourke, the principal research fellow at Sheffield Hallam University who is leading the study, says we have yet to understand fully the mechanisms behind the cancer-fighting power of exercise.
"There are indications from studies of humans that indicate that exercise may benefit the genes that control cell replication," he says. "Cancer occurs when the process of cell replication goes awry."
Dr Bourke's study also aims to find the 'sweet spot' for cancer patients, where they undertake enough exercise to gain benefits, but not do so much that it may pitch them into suffering fatigue.
The evidence so far shows that comparatively gentle exercise is most effective. "You don't have to be an athlete to get the benefits," says Dr Bourke.