Pierre Jacques Antoine Béchamp (October 16, 1816 – April 15, 1908) was a French chemist and biologist now best known as a rival of Louis Pasteur. Béchamp did pioneering work in industrial chemistry, developing an efficient process to produce aniline dye which was central to the development of the synthetic dye industry. He also developed p-aminophenylarsonate, an organic arsenic compound used to treat parasitic diseases.
Béchamp's later life was consumed by a bitter and protracted dispute with Louis Pasteur. Initially, their rivalry centered on credit for discovery of fermentation and later grew to encompass competing ideas on microbiology, pathogenesis, and germ theory. Béchamp believed that living entities called "microzymes" created bacteria in response to host and environmental factors; he did not believe that bacteria could invade a healthy host and create disease on their own. Pasteur's competing vision became widely accepted by scientists, and Béchamp sank into obscurity, although his beliefs have been continuously promoted by a small fringe of dedicated advocates.
Otto Heinrich Warburg (October 8, 1883 – August 1, 1970), son of physicist Emil Warburg, was a German physiologist, medical doctor and Nobel laureate. He served as an officer in the elite Uhlan (cavalry regiment) during the First World War, and won the Iron Cross (1st Class) for bravery. Warburg was one of the 20th century's leading biochemists. He won the Nobel Prize of 1931. In total, he was nominated an unprecedented three times for the Nobel prize for three separate achievements.
Warburg investigated the metabolism of tumors and the respiration of cells, particularly cancer cells, and in 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme." The award came after receiving 46 nominations over a period of nine years beginning in 1923, 13 of which were submitted in 1931, the year he won the prize.
In 1924, Warburg hypothesized that cancer, malignant growth, and tumor growth are caused by tumor cells mainly generating energy (as e.g. adenosine triphosphate / ATP) by nonoxidative breakdown of glucose (a process called glycolysis) and the subsequent recycling of the metabolite NADH back to its oxidized form, for reuse in the glycolytic cycle to complete the process (known as fermentation, or anaerobic respiration). This is in contrast to "healthy" cells, which mainly generate energy from oxidative breakdown of pyruvate. Pyruvate is an end product of glycolysis, and is oxidized within the mitochondria. Hence, and according to Warburg, cancer should be interpreted as a mitochondrial dysfunction.
"Cancer, above all other diseases, has countless secondary causes. But, even for cancer, there is only one prime cause. Summarized in a few words, the prime cause of cancer is the replacement of the respiration of oxygen in normal body cells by a fermentation of sugar." -- Dr. Otto H. Warburg in Lecture 
Warburg continued to develop the hypothesis experimentally, and held several prominent lectures outlining the theory and the data.
The concept that cancer cells switch to fermentation in lieu of aerobic respiration has become widely accepted, even if it is not seen as the cause of cancer. Some suggest the Warburg phenomenon could be used to develop anticancer drugs. Meanwhile, cancer cell glycolysis is the basis of positron emission tomography (18-FDG PET), a medical imaging technology that relies on this phenomenon.
Royal Raymond Rife (May 16, 1888 – August 5, 1971) was an American inventor and early exponent of high-magnification time-lapse cine-micrography. In the 1930s, he claimed that by using a specially designed optical microscope, he could observe a number of microbes which were too small to visualize with previously existing technology. Rife also reported that a 'beam ray' device of his invention could weaken or destroy the pathogens by energetically exciting destructive resonances in their constituent chemicals.
Rife's claims could not be independently replicated,  and were ultimately discredited by the medical profession in the 1950s. Rife blamed the scientific rejection of his claims on a conspiracy involving the American Medical Association (AMA), the Department of Public Health, and other elements of "organized medicine", which had "brainwashed" potential supporters of his devices.
Interest in Rife's claims was revived in some alternative medical circles by the 1987 book "The Cancer Cure That Worked", which claimed that Rife had succeeded in curing cancer, but that his work was suppressed by a powerful conspiracy headed by the AMA.
In his 1971 State of the Union speech, President Richard Nixon declared war on cancer, prompting passage of the National Cancer Act, aimed at making the "conquest of cancer a national crusade." Just four years later, scientists from the National Cancer Institute published a study demonstrating that a group of compounds taken from a common, widely cultivated plant shrank lung tumors that had been implanted in mice, extending their survival