Researchers working under the direction of Allison and Honjo discovered methods of removing constraints on "T cells" that fight invaders by modulating immune responses.
Many of Allison's patients are alive and cancer free because of his approach.
Allison, who is a professor at the University of Texas MD Anderson Cancer Center, Houston, was studying a protein called CTLA-4 that inhibits a person's immune system by putting the brakes on the actions of T cells.
Allison and Honjo's work had both worked on proteins that act as brakes on the immune system - preventing the body and its main immune cells, known as T-cells, from attacking tumour cells effectively. "I didn't set out to study cancer, but to understand the biology of T cells, these incredible cells [that] travel our bodies and work to protect us".
James Allison and Tasuku Honjo have jointly received the Nobel Prize in physiology or medicine for their work on immune checkpoints. To take CTLA-4 as an example, Allison's work was part of a sequence of advances starting before Ron Schwartz and Marc Jenkins' work on costimulatory signals and running beyond Nils Lonberg's involvement in the development of the ipilimumab molecule. The result is dramatically improved outcomes for some cancer patients and an explosion of research into ways to build on progress made to date.
"By stimulating the ability of our immune system to attack tumor cells, this year's #NobelPrize laureates have established an entirely new principle for cancer therapy".
Antibodies against PD-1 have been approved by the US Food and Drug Administration as an investigational new drug for the treatment of cancer.
Seal attacks kayaker with octopus
He told Yahoo 7 News that he and his kayaking buds had been watching the seal and the octopus fighting for quite a while. The seal then disappears back into the water before going on to dive in between other kayakers.
Allison's research was conducted at the University of California, Berkeley.
The Nobel jury said that "for more than 100 years, scientists attempted to engage the immune system in the fight against cancer".
He said Allison's work a decade ago "really opened up immunotherapy" as a fifth pillar of cancer treatments, after surgery, radiation, chemotherapy and precision therapy.
Prof Honjo said the award came "completely out of the blue" and "of course, I was very happy, delighted at the same time, but shocked". Carter announced in 2016 that he no longer needed treatment. "Therapies based on his discovery proved to be strikingly effective in the fight against cancer".
Arnault, 72, is married to a member of the Swedish Academy which selects the Nobel Literature Prize victor, and his cultural club Forum received generous funding from the Academy.
The prizes for physics, chemistry, and peace will also be announced this week.
The literature prize will not be handed out this year after the awarding body was hit by a sexual misconduct scandal.