What is the cure for cancer? Well, it appears that's not the correct way to look at the problem. Cancer isn't one thing. There isn't one disease process that causes every form of cancer. Some cancers seem to occur for no reason at all, while there are other causes like smoking that are documented to be cancer-causing. Even within the same kind of cancer, for example ovarian cancer, there are different presentations of the disease depending on the patient's other health issues and physical condition.
The reason each cancer is different is that each type of cancer is the result of genetic mutations. The genomes for every kind of cancer have not been fully mapped, so there's currently know what to look at each type of cancer and know how gene expression will go wrong. Chemotherapy and radiation can shut down rogue cell growth and mutations, however it will usually damage nearby healthy cells as well. And so it goes, the goal of curing cancer is likely to be a long haul event. Check out this video to get a detailed, yet easy to understand explanation of the process.